It would be very difficult to checkmate the strongest piece on the board
How to play this variant on chess.com
You can checkmate either the king or queen. So you can checkmate the king as normally. If the king and queen are ever forked, it is also a checkmate, since you can't place your queen in check. It leads to interesting games because one has ones queen for the entire game, however the queen is in effect much less powerful since she cannot put herself into danger. It's a very fun variant.
How to play a variant on chess.com with the following rule changes:
Both king and queen are royal. (You cannot place your king or queen in check, and one or both can be checkmated.)
Queen can also short castle.