What Ive found to work out really well, and in my opinion is THE cheapest way to fix this is to go to wal-mart, head for the paint section, and grap a roll of double sided mounting tape. take you plate off (along with any plate frames) and put 2 layers of the tape around the perimiter of the plate. this will keep you plate from ever touching your car, so you can forget any chance of rattle, plus the foam from the tape will obsorb any vibrations.

 

is the frame necessary? thats what is killin ya. the plate itself doesnt rattle that bad. at least on mine i dont think.

 

I used a sponge on my old car and that worked well. Just wedge it behind the plate.