Rinse peaches; cut each in half and pit. In a 9- to 10-inch frying pan over medium-high heat, melt butter; add sugar and stir until well blended. Remove pan from heat, set peaches in butter mixture, and turn them to coat evenly.
Lay peaches, cut side down, on a barbecue grill over a solid bed of medium coals or medium heat on a gas grill (you can hold your hand at grill level only 4 to 5 seconds); close lid on gas grill. Cook until peaches are hot and lightly browned on the bottom. Brush tops with more butter mixture, then turn fruit over and brush cooked sides with mixture. Cook until peaches are warm but still hold their shape, 6 to 10 minutes total.