In a small saucepan over low heat, combine the butter, herbes de Provence, garlic and 1/4 teaspoon salt. Heat until melted and beginning to brown, about 8 minutes. Remove from the heat and set aside for 15 minutes to allow the flavors to infuse.
Meanwhile, place the clams directly on the hot grill. Close the lid and cook until the clams pop open, 6 to 8 minutes. Remove the clams to a platter and serve with crusty bread and herb butter for dipping.