You don't want to make being praised unpleasant for the recipient -- that leads to perverse incentives. And you don't want to give an award a stupid name or an embarrassing shape -- part of the point of this sort of thing is that it looks good on your resume or perched over your desk. You want to mark their achievement in a way they'll genuinely appreciate, but simultaneously add symbolism to make their coworkers feel that their status hasn't been diminished.

I think what you're looking for is a little temporary public humiliation, not intrinsic to the award but coming along with more standard recognition. You could do this in several different ways. If it's a fairly small group and the awards are a fairly big deal, for example, you could run a roast as part of the party following the award. You could probably contrive ways to add this kind of symbolism to physical awards, too.