Preheat a grill to high. Toss the tomatoes with the melted butter, wine, tarragon, 1/2 teaspoon salt and a few grinds of pepper. Pile the tomatoes in the center of a 24-inch-long piece of foil. Gather the edges and crimp to seal and form a packet.
Brush the grill grates with vegetable oil. Brush both sides of the fish with vegetable oil; season generously with salt and pepper. Place the fish on one side of the grill, skin-side down. Grill until the fish is cooked through, 5 to 6 minutes per side. Meanwhile, grill the tomato packet on the other side of the grill, undisturbed, until the tomatoes are softened, 10 to 12 minutes.
Carefully open the foil packet. Spoon the tomatoes and their juices over the fish and top with more tarragon.