Preheat oven to 200º.
Cover a large baking sheet with parchment paper. Draw a 14 x 10-inch rectangle on paper. Turn paper over; secure with masking tape.
Place egg whites and cream of tartar in a large bowl, and beat with a mixer at medium speed until soft peaks form. Increase speed to high, and gradually add granulated sugar and then powdered sugar, 1 tablespoon at a time, beating until stiff peaks form. Add extract; beat just until blended. Fold in cherries and chocolate. Spread batter onto drawn rectangle using the back of a spoon. Score rectangle into 2-inch squares using the tip of a sharp knife.
Bake at 200º for 2 hours. Turn oven off, and cool meringue in closed oven 1 1/2 hours or until dry. Carefully remove meringue from paper. Break into (2-inch) squares.