You can stop license plate rattle with the Dynamat Xtreme License Plate Kit. The kit includes a sheet of Dynamat Xtreme for the back of the license plate.
Dynamat 19100 Xtreme License Plate Kit
Kit contains one 4 in x 10 in piece of Dynamat Xtreme to be used on the back of the license plate plus four foam strips for attaching the included decorative frame. For proper installation, use a Dynaroller tool.