Rub a cold skillet with 1 tablespoon of cold butter. Lightly score the duck breasts through the skin only in a cross-hatch pattern. Season breasts with salt and pepper on both sides and place in cold skillet, skin sides down. Turn heat to medium/medium-high and cook until crispy, about 13 minutes. Drain off most of the fat and discard. Turn breasts over and cook for another 2 minutes.
While breasts are cooking, put the cherries and their juices into a sauce pan and add the balsamic vinegar, a small pinch of salt and a large pinch of pepper. Cook over medium-high heat, stirring occasionally, until the juices have reduced down to an almost syrup-like consistency and the cherries are starting to break apart. About 15 minutes. Take off heat and stir in 1 tablespoon of cold butter to finish the sauce. Serve sauce with duck breast and rice pilaf.