There used to be directories of sites that gave out site awards but all that I know of died out. Most of the sites giving general awards were just doing it to gain incoming links and increase their own traffic when a recipient posted their award graphic. In other words, anyone could "win" the award.
With that said, finding a large site covering your subject that gives out awards could prove beneficial if they promote their awards. For example, I know some About.com guides used to give out a "best of the year" type awards. The guides would announce the upcoming awards, build interest with their audience, and then provide a nice write-up of the yearly winners. This could drive some highly targeted traffic to a site.
Ok, I know Lisa and most of you already realize all that,
but I just wanted to use About.com as an example.
On the reverse side of the coin, you could always set up your own award to hand out.
Anyway, I'm tired and rambling (what's new??) but here are a few sources for you to check: