user-1: I was asked for first time to help at a non federated tournament for kids to arbitrate their games, played at 30 minutes with no increment time.
It was a scholar tournament and they made mistakes as leaving checkmates in one, let the queen to be captured etc.
At one game both kids arrived to a K+R K+R endgame. There was not a way to quickly gain the rook and win the game and both kids had time.
One kid claimed it was a draw. We were two arbiters (not experts, just two 1900 helping a bit at the club).
We claimed draw.
Was it a correct decision or we should have left the kids play?

user13433: Relevant FIDE rule, appendix G.5:

If Article G.4 [a player may claim extra time for both sides] does not apply and the player having the move has less
  than two minutes left on his clock, he may claim a draw before his
  flag falls. He shall summon the arbiter and may stop the chessclock
  (see Article 6.12 b). He may claim on the basis that his opponent
  cannot win by normal means, and/or that his opponent has been making
  no effort to win by normal means.

Similar to the USCF rule cited by D M, technically this can only be invoked if the claiming player has less then two minutes on their clock. 

user12629: It is difficult to say what the exact rules should be if you aren't affiliated with a group that publishes rules for such situations. But I think your actions in this case were reasonable.
USCF rule 14H used to state that a player with less than two minutes on the clock (with no delay or increment being used) could make a claim of insufficient losing chances. Officially, that rule is no longer in effect, although a tournament is still allowed to use it as a variation without announcing it in advance. 
If this variation is used, then rule 14I4 specifically states that rook vs rook should be a draw unless it is a position where there is a quick win. In general, if a class C player with ample time would not reasonably lose the position against a master, then the draw claim would be upheld, under this variation. This is regardless of the actual strengths of the players involved or how little time is on the clock.
Since there were more than 2 minutes on the clock ("both kids had time") technically this variation could not have been invoked. However, an attempted draw claim also constitutes a draw offer, which the other player may accept even if the claim is not upheld. According to your comment on another answer, you asked the other player if they agreed with the draw, and they seemed happy with it. That would be good enough for me. If neither player wanted to play on, there would be little point in forcing them to shuffle the pieces around for 50 moves. It's possible that novice players would not even be aware of the possibility of simply offering a draw.
The part of the USCF Official Rules of Chess book which contains the rules is now available online, by the way. I found it here.

user12873: It's better to let them play it out a bit and ideally only draw once reaching 50 moves. But if one of them is low on time (and their opponent is clearly just trying to flag them) then you should claim the draw.

user12523: It is not a drawn position according to the rules, since there is sufficient mating material. It may be a draw from the point of view of endgame theory, but given players who make lots of mistakes, it wouldn't be all that surprising for one to lose to a tactic.
I would let them play until the player who wanted a draw can claim it based on the 50-move rule or threefold repetition, or someone runs out of time or the game ends some other way. (Were they keeping notation? If not making a proper claim could be difficult, although an arbiter who witnesses the game could rule it a draw after 75 moves or fivefold repetition. Also note that USCF rules allow the arbiter or a deputy to count moves, if requested, for a 50-move claim under sudden death.)
That said, for a "non federated kids tournament", I suppose you may have some leeway, so I wouldn't really fault you for ruling it a draw.

user4418: You can declare a draw and in fact you are required to declare a draw but only after you have counted 75 moves by each side without a capture or a pawn move. This is according to the FIDE Laws of Chess article 9.6.2:

9.6 If one or both of the following occur(s) then the game is drawn:
9.6.1 the same position has appeared, as in 9.2.2 at least five times.
9.6.2 any series of at least 75 moves have been made by each player without the movement of any pawn and without any capture. If the last
  move resulted in checkmate, that shall take precedence

Of course the players are also free to agree a draw between them.
EDIT: blues makes the following comment:

III.5.1 may also apply. If the arbiter agrees that the opponent cannot
  win by normal means, or that the opponent has been making no effort to
  win the game by normal means, he shall declare the game drawn.
  Otherwise he shall postpone his decision or reject the claim. This
  does not require 75 moves or fivefold repetition

I will answer that here since there is insufficient room in a comment to do so.
Guidelines III.5.1 almost certainly does not apply in this case. III.5.1 is not standalone. It is part of section III and is dependent on earlier parts of III.
Let's take a look.

Guidelines III. Games without increment including Quickplay Finishes
III.1 A ‘quickplay finish’ is the phase of a game when all the remaining moves must be completed in a finite time.
III.2.1 The Guidelines below concerning the final period of the game including Quickplay Finishes, shall only be used at an event if their
  use has been announced beforehand.
III.2.2 These Guidelines shall apply only to standard chess and rapid chess games without increment and not to blitz games.

First, according to the OP, the time control was all moves in 30 minutes, so a rapid time control and no increments mean it is possible that III applies. However according to III.2.1 these shall only be used at an event if their use has been announced beforehand. They were almost certainly not announced beforehand, else the two arbiters would have at least know of their existence and they appear not to.
Suppose they were announced beforehand. Then we come to: 

III.4 If the player having the move has less than two minutes left on
  his clock, he may request that an increment extra five seconds be
  introduced for both players. This constitutes the offer of a draw. If
  the offer refused, and the arbiter agrees to the request, the clocks
  shall then be set with the extra time; the opponent shall be awarded
  two extra minutes and the game shall continue.

The OP in one of his comments seems to say that both players still had 25 minutes left. This would mean this does not apply. Nevertheless supposing the player did have less than 2 minutes left, the arbiters cannot apply this rule unless the player specifically asks for it. The arbiters are not allowed to help the players in any way and may not volunteer this information during the game. They may only make announcements informing all players before the game. 
Continuing, we finally reach the part blues references:

III.5 If Article III.4 does not apply and the player having the move has less than two minutes left on his clock, he may claim a draw
  before his flag falls. He shall summon the arbiter and may stop the
  chessclock (see Article 6.12.2). He may claim on the basis that his
  opponent cannot win by normal means, and/or that his opponent has been
  making no effort to win by normal means

First, this can only apply if III.4 does not apply. The only way that can happen is if there are no digital clocks capable of being set with the required time and increment. If such clocks are available then III.4 applies and III.5 does not apply.
Suppose, however, that all the previous counterfactual "if onlys" apply then III.5 can only apply if the player also knows the rule and makes the specific request in the correct manner. Again, even if the arbiter knows the rule he may not help the player by volunteering the information.
Hence my original conclusion that - Guidelines III.5.1 almost certainly does not apply in this case.

-1: <p>I was asked for first time to help at a non federated tournament for kids to arbitrate their games, played at 30 minutes with no increment time.
It was a scholar tournament and they made mistakes as leaving checkmates in one, let the queen to be captured etc.</p>

<p>At one game both kids arrived to a K+R K+R endgame. There was not a way to quickly gain the rook and win the game and both kids had time.
One kid claimed it was a draw. We were two arbiters (not experts, just two 1900 helping a bit at the club).
We claimed draw.</p>

<p>Was it a correct decision or we should have left the kids play?</p>
 13433: <p>Relevant FIDE rule, appendix G.5:</p>

<blockquote>
  <p>If Article G.4 [a player may claim extra time for both sides] does not apply and the player having the move has less
  than two minutes left on his clock, he may claim a draw before his
  flag falls. He shall summon the arbiter and may stop the chessclock
  (see Article 6.12 b). He may claim on the basis that his opponent
  cannot win by normal means, and/or that his opponent has been making
  no effort to win by normal means.</p>
</blockquote>

<p>Similar to the USCF rule cited by D M, technically this can only be invoked if the claiming player has less then two minutes on their clock. </p>
 12629: <p>It is difficult to say what the exact rules should be if you aren't affiliated with a group that publishes rules for such situations. But I think your actions in this case were reasonable.</p>

<p>USCF rule 14H used to state that a player with less than two minutes on the clock (with no delay or increment being used) could make a claim of insufficient losing chances. Officially, that rule is no longer in effect, although a tournament is still allowed to use it as a variation without announcing it in advance. </p>

<p>If this variation is used, then rule 14I4 specifically states that rook vs rook should be a draw unless it is a position where there is a quick win. In general, if a class C player with ample time would not reasonably lose the position against a master, then the draw claim would be upheld, under this variation. This is regardless of the actual strengths of the players involved or how little time is on the clock.</p>

<p>Since there were more than 2 minutes on the clock ("both kids had time") technically this variation could not have been invoked. However, an attempted draw <em>claim</em> also constitutes a draw <em>offer</em>, which the other player may accept even if the claim is not upheld. According to your comment on another answer, you asked the other player if they agreed with the draw, and they seemed happy with it. That would be good enough for me. If neither player wanted to play on, there would be little point in forcing them to shuffle the pieces around for 50 moves. It's possible that novice players would not even be aware of the possibility of simply offering a draw.</p>

<p>The part of the USCF Official Rules of Chess book which contains the rules is now available online, by the way. I found it <a href="http://www.uschess.org/content/view/7752/369/" rel="noreferrer">here</a>.</p>
 12873: <p>It's better to let them play it out a bit and ideally only draw once reaching 50 moves. But if one of them is low on time (and their opponent is clearly just trying to flag them) then you should claim the draw.</p>
 12523: <p>It is not a drawn position according to the rules, since there is sufficient mating material. It may be a draw from the point of view of endgame theory, but given players who make lots of mistakes, it wouldn't be all that surprising for one to lose to a tactic.</p>

<p>I would let them play until the player who wanted a draw can claim it based on the 50-move rule or threefold repetition, or someone runs out of time or the game ends some other way. (Were they keeping notation? If not making a proper claim could be difficult, although an arbiter who witnesses the game could rule it a draw after 75 moves or fivefold repetition. Also note that USCF rules allow the arbiter or a deputy to count moves, if requested, for a 50-move claim under sudden death.)</p>

<p>That said, for a "non federated kids tournament", I suppose you may have some leeway, so I wouldn't really fault you for ruling it a draw.</p>
 4418: <p>You can declare a draw and in fact you are required to declare a draw but only after you have counted 75 moves by each side without a capture or a pawn move. This is according to the <a href="https://www.fide.com/fide/handbook.html?id=208&amp;view=article" rel="nofollow noreferrer">FIDE Laws of Chess</a> article 9.6.2:</p>

<blockquote>
  <p>9.6 <strong>If one or both of the following occur(s) then the game is drawn:</strong></p>
  
  <p>9.6.1 the same position has appeared, as in 9.2.2 at least five times.</p>
  
  <p>9.6.2 <strong>any series of at least 75 moves have been made by each player without the movement of any pawn and without any capture. If the last
  move resulted in checkmate, that shall take precedence</strong></p>
</blockquote>

<p>Of course the players are also free to agree a draw between them.</p>

<p>EDIT: blues makes the following comment:</p>

<blockquote>
  <p>III.5.1 may also apply. If the arbiter agrees that the opponent cannot
  win by normal means, or that the opponent has been making no effort to
  win the game by normal means, he shall declare the game drawn.
  Otherwise he shall postpone his decision or reject the claim. This
  does not require 75 moves or fivefold repetition</p>
</blockquote>

<p>I will answer that here since there is insufficient room in a comment to do so.</p>

<p>Guidelines III.5.1 almost certainly does not apply in this case. III.5.1 is not standalone. It is part of section III and is dependent on earlier parts of III.</p>

<p>Let's take a look.</p>

<blockquote>
  <p><strong>Guidelines III. Games without increment including Quickplay Finishes</strong></p>
  
  <p><strong>III.1</strong> A ‘quickplay finish’ is the phase of a game when all the remaining moves must be completed in a finite time.</p>
  
  <p><strong>III.2.1 The Guidelines below concerning the final period of the game including Quickplay Finishes, shall only be used at an event if their
  use has been announced beforehand.</strong></p>
  
  <p><strong>III.2.2</strong> These Guidelines shall apply only to standard chess and rapid chess games without increment and not to blitz games.</p>
</blockquote>

<p>First, according to the OP, the time control was all moves in 30 minutes, so a rapid time control and no increments mean it is possible that III applies. However according to III.2.1 these <strong>shall only be used at an event if their use has been announced beforehand</strong>. They were almost certainly <strong>not</strong> announced beforehand, else the two arbiters would have at least know of their existence and they appear not to.</p>

<p>Suppose they were announced beforehand. Then we come to: </p>

<blockquote>
  <p><strong>III.4</strong> If the player having the move has <strong>less than two minutes</strong> left on
  his clock, he may request that an increment extra five seconds be
  introduced for both players. This constitutes the offer of a draw. If
  the offer refused, and the arbiter agrees to the request, the clocks
  shall then be set with the extra time; the opponent shall be awarded
  two extra minutes and the game shall continue.</p>
</blockquote>

<p>The OP in one of his comments seems to say that both players still had 25 minutes left. This would mean this does not apply. Nevertheless supposing the player did have less than 2 minutes left, the arbiters cannot apply this rule unless the player specifically asks for it. The arbiters are not allowed to help the players in any way and may not volunteer this information during the game. They may only make announcements informing all players <strong>before</strong> the game. </p>

<p>Continuing, we finally reach the part blues references:</p>

<blockquote>
  <p><strong>III.5</strong> If Article III.4 does not apply and the player having the move has less than two minutes left on his clock, he may claim a draw
  before his flag falls. He shall summon the arbiter and may stop the
  chessclock (see Article 6.12.2). He may claim on the basis that his
  opponent cannot win by normal means, and/or that his opponent has been
  making no effort to win by normal means</p>
</blockquote>

<p>First, this can only apply if III.4 does not apply. The only way that can happen is if there are no digital clocks capable of being set with the required time and increment. If such clocks are available then III.4 applies and III.5 does not apply.</p>

<p>Suppose, however, that all the previous counterfactual "if onlys" apply then III.5 can only apply if the player also knows the rule and makes the specific request in the correct manner. Again, even if the arbiter knows the rule he may not help the player by volunteering the information.</p>

<p>Hence my original conclusion that - Guidelines III.5.1 almost certainly does not apply in this case.</p>
