In a large, wide bowl or 9- by 13-inch baking dish, stir brown sugar, wine, lemon juice, 1/2 teaspoon salt, and 1/4 teaspoon pepper until sugar is dissolved.
Rinse fish and pat dry. Add to marinade and turn to coat. Cover and chill for 1 to 2 hours.
Lift salmon from marinade and transfer to a 12- by 17-inch baking pan. Pour marinade into a 1 1/2- to 2-quart pan over medium-high heat; add butter and stir until butter is melted and mixture is simmering, 4 to 5 minutes.
Lay salmon, skinned side down, on a generously oiled grill over a solid bed of medium-hot coals or medium-high heat on a gas grill (you can hold your hand at grill level only 3 to 4 seconds). Brush fish generously with the baste; close lid if using a gas grill. Cook until salmon pieces are well browned on the bottom, 3 1/2 to 4 minutes (keep a spray bottle filled with clean water on hand to spritz any flare-ups). With a wide spatula, carefully turn pieces; brush tops with baste and continue to cook, basting often, until the salmon is just opaque but still moist-looking in the center of the thickest part (cut to test), about 5 to 6 minutes longer. Discard any remaining baste.
Transfer salmon to a warm platter or plates and garnish with lemon wedges. Add more salt and pepper to taste.