Pat the chops dry, and rub them all over with a mixture of the rosemary, salt, pepper and garlic. Cover, and marinate for up to 2 hours at room temperature, or overnight in the refrigerator. Bring the chops back to room temperature before grilling.
Heat one side of a charcoal or gas grill, and put the rack about 4 inches from the heat source. Cook the chops over the hottest part of the fire until well seared on both sides, about 2 or 3 minutes per side. Move them to the cool part of the grill, cover and cook until done, anywhere from 1 to 3 minutes, depending on the heat of the fire and the thickness of the chops. The pork is done when it’s just firm to the touch, its juices run just slightly pink and the meat is rosy in the center, or when an instant-read thermometer registers 135 degrees in the thickest part of the chop (the temperature will continue to rise as the chops rest). Transfer them to a platter, cover loosely with aluminum foil and let them rest while you make the sauce.
Put 1 tablespoon of the butter in a skillet over medium-high heat. When the foam subsides, add the shallots, and cook until soft, 2 or 3 minutes. Add the cherries, wine and whatever juices have accumulated around the pork chops; cook, stirring occasionally, until the liquid reduces into a thin syrup, 5 or 6 minutes. Stir in the remaining 2 tablespoons butter, a little at a time, until it’s incorporated into the sauce. Season with salt and pepper. Pour the sauce over the chops, and serve.