It can be difficult to dry every nook and cranny of a cookie cutter after you've washed it, leaving those made of tin or copper more likely to rust or tarnish. Spread just-washed cutters on a clean baking sheet, and place them in the oven (while it's still warm) for several minutes. The heat will evaporate any excess moisture. Remove, and cool thoroughly.
Drying Cookie Cutters
Martha Stewart Living, December 2004