Prepare Cherries: Drain Cherries and stuff one or two chocolate chips into each. Set aside.
In a large bowl, cream shortening and sugar. Add eggs and vanilla. Mix well. Sift flour, baking soda and salt. Add one third of the dry ingredients at a time, and mix well after each addition. Refrigerate for one half hour.
When ready to make cookies, take enough dough to form a one-inch ball. Pull apart into fairly even halfs. Place a stuffed cherry between halfs and mold around cherry until it is completely covered. Roll between hands to create a smooth ball.
Bake in 350 degree oven for 11-16 minutes. Dough should be firm but not hard. (Note: some ovens can make this a fast bake, 7-9 minutes, so keep an eye on it and time based on your oven).
While still hot roll in powdered sugar. Optionally, then roll in red and green sugar. Be careful with this step as cookies are fragile and can crack open.
Alternately, cool cookie then drizzle with powdered sugar glaze, then sprinkle with red and green sugars.