Drain cherries and set on paper towels to dry.
In a medium bowl, combine butter and corn syrup until smooth. Stir in confectioners’ sugar and knead to form a dough. Chill to stiffen if necessary. Wrap each cherry in about 1 teaspoon of dough. Chill until firm.
Melt 1 c. chocolate chips and shortening in a heavy saucepan over low heat. Dip each cherry in by its stem, and place on waxed paper lined sheets. Chill until completely set. Store in an airtight container in a cool place. Best after 1 or 2 weeks.