Combine the melted butter, parsley, lemon juice, salt, and pepper, and keep warm.

Prepare the grill for direct heat and preheat to high. Place the clams in a single layer directly on the grill rack. Grill just until the clams open – this will take between 5 – 10 minutes. Using tongs, carefully remove the clam shells from the grill and place them on a serving platter, trying not to lose the liquid inside the shells. Discard any clams that do not open. Spoon a little of the lemon butter into each clam and serve with lemon wedges.