Heat oven to 400°F. In large bowl, beat butter with electric mixer on medium speed until fluffy. Gradually beat in 1/2 cup powdered sugar until light and fluffy. Stir in almond extract. In medium bowl, mix flour and salt. On low speed, beat flour mixture into butter mixture until well blended. Stir in cherries.
Shape dough into 1-inch balls. On ungreased cookie sheet, place balls 2 inches apart.
Bake 9 to 11 minutes or until edges just begin to brown. Cool slightly. Measure 1/2 cup powdered sugar into small bowl. Roll each cookie in powdered sugar. Place on cooling rack to cool completely.
Place chocolate chips in small resealable freezer plastic bag. Microwave on High 45 to 60 seconds, turning bag over every 20 seconds. Squeeze bag until chips are melted and smooth. Cut small tip off one corner of bag, and drizzle over cooled cookies. Let stand at room temperature at least 30 minutes until chocolate hardens before storing.