In mixing bowl, combine sugar, butter, milk, and extract; mix well. Knead into large ball. Roll into 1 inch balls and flatten each into 2 inch circle. Wrap around cherries and lightly roll in hands. Place with stem up on waxed paper-lined baking sheet. Cover loosely and refrigerate 4 hours or over night. Melt the chocolate chips and shortening in a double-boiler or microwave-safe bowl. Holding onto stem, dip cherries into chocolate; set on waxed paper to harden. Store in a covered container. Refrigerate 1-2 weeks before serving. The longer the candies sit the juicier the center will be.
*We have found that the cheap brand of cherries make a very dry cherry so you may not want to drain them much. If you end up with a dry filling store them on the counter for a week, which seems to help some.