Line a cookie sheet with parchment paper or waxed paper. Pat cherries dry with paper towels.
Melt chocolates separately in stainless steel bowl set over pan of simmering water, stirring until smooth.
Holding stem of cherry, dip cherry into melted chocolate to coat. You can coat half of cherry in white chocolate and half in semisweet chocolate, if desired. Transfer chocolate-dipped cherry to prepared cookie sheet. Repeat with remaining cherries and melted chocolate.