Place oven rack in middle position of the oven.
Preheat oven to 350 degrees F.
In a medium bowl, combine flour and nutmeg; set aside. In a large bowl, beat butter, shortening and extracts with an electric mixer until smooth.
Gradually add sugar to butter mixture and cream until mixture is light. Blend in flour mixture. Dough should be slightly moist. If dough looks dry, sprinkle with water and work into dough. If dough is sticky, sprinkle with additional flour.
Spoon dough by teaspoons and form into balls.
Place on an ungreased baking sheet. Gently press each ball with palm of hand to form cookie.
Cut each cherry into 8 pieces. Garnish with a cherry piece placed in the center of each cookie.
Bake 20 minutes or until golden. Cool cookies on a wire rack.