user2785: This happened to me yesterday.  It was unreasonable for me to play on, so I was going to resign but my opponent was not at the board.  They probably left the board to watch another game, waiting for my next move.
Question:  What is the correct way to resign if my opponent is not at the board?
I stopped the clock, wrote 1-0 on my scoresheet (I was black), and started resetting the pieces.  But this doesn't strike me as an officially correct thing to do.

user3270: That's an acceptable way to do it. If you want a more official record, sign your scoresheet after writing 1-0. I usually motion for them to come back to the board and then offer a handshake.

user550: I agree with Cleveland that what you did is probably sufficient. One other thing you can always do if you can't find the opponent and are concerned that you might be seen as doing something suspicious is to call the arbiter and announce your resignation to them. 

user9684: When my opponent is at the board, I signal my resignation by handing him/her/it my King.  When my opponent is not at the board, I signal my resignation by placing both King on the center squares.  The dark squares if I played White, and the light squares if I played Black.  I do stop and try to shut off the clock.  I consider it bad etiquette to pick up his/her/its personal property, the chess case.  Normally, I have plenty of time and can wait for my opponent to return and help put away the set.
It is good practice to have both players mark the score on the wall chart and to analyse the game, whatever the outcome of the game. "People who want to improve should take their defeats as lessons, and endeavor to learn what to avoid in the future." Capablanca.

2785: <p>This happened to me yesterday.  It was unreasonable for me to play on, so I was going to resign but my opponent was not at the board.  They probably left the board to watch another game, waiting for my next move.</p>

<p><em>Question</em>:  What is the correct way to resign if my opponent is not at the board?</p>

<p>I stopped the clock, wrote 1-0 on my scoresheet (I was black), and started resetting the pieces.  But this doesn't strike me as an officially correct thing to do.</p>
 3270: <p>That's an acceptable way to do it. If you want a more official record, sign your scoresheet after writing 1-0. I usually motion for them to come back to the board and then offer a handshake.</p>
 550: <p>I agree with Cleveland that what you did is probably sufficient. One other thing you can always do if you can't find the opponent and are concerned that you might be seen as doing something suspicious is to call the arbiter and announce your resignation to them. </p>
 9684: <p>When my opponent is at the board, I signal my resignation by handing him/her/it my King.  When my opponent is not at the board, I signal my resignation by placing both King on the center squares.  The dark squares if I played White, and the light squares if I played Black.  I do stop and try to shut off the clock.  I consider it bad etiquette to pick up his/her/its personal property, the chess case.  Normally, I have plenty of time and can wait for my opponent to return and help put away the set.</p>

<p>It is good practice to have both players mark the score on the wall chart and to analyse the game, whatever the outcome of the game. "People who want to improve should take their defeats as lessons, and endeavor to learn what to avoid in the future." Capablanca.</p>
