Cut the peaches in half and remove the pit: With a sharp paring knife, slice each peach in half. Then twist each half in opposite directions to pull the halves apart. Use your fingers to remove the pit. If it's stuck, carefully slide the knife under the pit and then pull it away.
Brush the peaches all over with the melted butter.
Place the peaches, cut side down, on the grill. Grill until tender and slightly charred, about 4 minutes per side. Serve immediately.