How to get a draw...

I have just played this game and think its an good example on what to avoid and what strategy to follow in an objectively hopeless endgame... but ofcourse it must build on some kind of mistake from the opponent:

You played well. I always think there is a chance of a draw if you have a queen.

However, in this case black can win with 45. ... f4+  when

46. Qxf4 Qxf4 or

46. Kf3 Qe3+ or

45. Kh3 Qe3+ 

I agree with you... and somehow I think my opponent got blind of the idea of some beautiful mate, instead of exchanging queens and then winning by "brute force".

60...f2 had been a strong move to, instead of h3??, with the threath of a mate on Qe4... But it is a good lesson to learn, that you haven't won until you have mated or your opponent surrender... And you should never lock your opponents last pawn ;-)