During the Doeberl Cup/SIO tournaments I witnessed 3 remarkable games that had one thing in common. They were Tindall v Toth from the Doeberl Cup Premier, Xie v Ghane (SIO) and Amrutha v Brown (SIO). In each case one player had 2 queens on the board, and remarkably, that player did not win the game. The only game where the 'stronger' side did not lose was the Xie Ghane game, but they may be attributed to the fact the Ghane had 2 extra rooks as well, giving him QQRR v QB for Xie. The other two games ended in wins for the 'weaker' side.
All three games can be found on the respective tournament websites (scroll down for posts containing the links), but here is the Amrutha v Brown game. The game had been 2R V Q for quite a while, and at various stages both sides could claim an advantage. Watching the game live I wasn't sure what was happening, but looking at it later I suspect that Brown especially played for a win, going so far as to risk losing on a number of occasions. This strategy finally paid off when Amrutha made a play for her second queen, not realising she had walked into a mate.
Amrutha,M (2155) - Brown,A (2085) [B33] Sydney International Open Parramatta, NSW (8.25), 18.04.2009
1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 e5 6.Ndb5 d6 7.Bg5 a6 8.Na3 b5 9.Bxf6 gxf6 10.Nd5 Bg7 11.Bd3 Ne7 12.Nxe7 Kxe7 13.0-0 d5 14.exd5 Qxd5 15.c4 bxc4 16.Nxc4 Rb8 17.Qe2 Qd4 18.Kh1 Be6 19.b3 f5 20.f3 e4 21.fxe4 fxe4 22.Bxe4 = 22...Qxa1 23.Rxa1 Bxa1 24.Na5 Rb5 25.Nc6+ Kf8 26.b4 Kg7 27.a4 Rg5 28.Qxa6 Re8 29.Qf1 Bc3 30.Qc1 Bf6 31.h3 Bxh3 32.gxh3 Rxe4 33.Qf1 Bc3 34.Qd3 Re1+ 35.Kh2 Bf6 36.b5 Ra1 37.Qe4 Ra2+ 38.Kh1 Rb2 39.Qf3 h5 40.Qe4 h4 41.Nd4 Rf2 42.Qd3 Kh8 43.b6 Rg3 44.Qe4 Rxh3+ 45.Kg1 Rb2 46.Nf5 Rg3+ 47.Nxg3 hxg3 48.b7 Kg7 49.Qg4+ Kf8 50.Qc8+ Kg7 51.b8Q (D)
51...Bd4+ 52.Kh1 Rh2# 0-1