Good Question! I teach chess for a living and many of my students are afraid of losing their Queens. I try to trade off Queens to release some of game's tension. You have a couple of options. However, the landscape of the board changes so much during a game that it's hard to say exactly what combination to use. Are you talking about having lost your Queen while your opponent has maintained their Queen? Are we talking endgame, where you're down to a few pieces?
If you lose your Queen while opponent maintains their Queen, go for paired attacks, such as a Bishop and Knight or Rook and Bishop. Can you clarify your question a little more?
Best ways to win without a queen?