Rangers fan Dale Hill, 21, from Belfast, was fined Â£200 after he admitted running on to the pitch.
Sentence on Celtic fan Sam Miller, 26, from Romford, Essex, was deferred after he admitted making sectarian remarks.
Robert Wyatt, 31, from Castlemilk, Glasgow, faces trial after he pleaded not guilty to running on to the pitch.
He appeared from custody and denied the breach of the peace charge.
A trial was set for October this year and bail was granted with the special conditions that he does not enter Hampden Park or attend any regulated football match in Scotland.
Rangers won the match 5-4 on penalties after the games ended 2-2 after extra time.
Three football fans have appeared in court having been arrested at Sunday's Scottish Cup semi-final between Celtic and Rangers at Hampden.