Have there been brilliancy prizes awarded to the losing player? Have there been brilliancy prizes awarded to the losing player? Preferably, it would be at a grandmaster level.
Not exactly a prize, but answers your question in spirit: Immortal Losing Game Wikipedia's summary of the game is:

The Immortal Losing Game is a chess game between the Soviet grandmaster David Bronstein and the Polish International Master Bogdan Śliwa played in 1957 in Gotha. The name is an allusion to the more famous Immortal Game between Adolf Anderssen and Lionel Kieseritzky. The game acquired its name because Bronstein, in a completely lost position, set a series of elegant traps in an attempt to swindle a victory from a lost game, although Śliwa deftly avoided the traps and won.