1. Heat oven to 425°F. In a medium bowl, mix flour, sugar, lemon peel, cream of tartar, baking soda, and salt. Cut in butter, using pastry blender (or pulling 2 table knives through ingredients in opposite directions), until mixture looks like fine crumbs. Stir in enough buttermilk so dough leaves the side of the bowl and forms a ball. Stir in cherries.
2. On an ungreased cookie sheet, drop dough by 1/3 cupfuls about 1 inch apart. Brush with milk.
3. Bake 10 to 15 minutes or until light brown. Immediately remove from cookie sheet and serve warm or cool.