Heat the oven to 425° F. Line 2 baking sheets with parchment paper.
In a large bowl, sift together the flour, baking soda, and baking powder. Add the salt, sugar, and cornmeal and mix together.
With a pastry cutter or a couple of butter knives, cut the butter into the flour mixture until it is the size of peas. Mix in the cherries, and then make a well in the center and pour in the buttermilk. Mix briefly, just until the dough comes together; it should be stiff and still a little sticky. (Don't worry about getting every last bit of flour.) Let rest for 5 minutes.
Form the dough into balls about 2 inches in diameter and place them on the baking sheets a couple of inches apart. Place in the oven and immediately turn down the temperature to 375° F. Bake for 20 to 25 minutes, rotating the sheets halfway through, until the scones are golden. Cool on a wire rack.