In a microwave-safe 9- by 13-inch baking dish, combine brown sugar, wine, soy sauce, butter, and lemon juice. Heat in a microwave oven at full power (100%) until boiling, about 2 minutes, stirring several times. Let cool 10 to 15 minutes.
Rinse salmon, pat dry, and lay skin side up in sugar-soy marinade. Cover and chill at least 1 hour or up to 1 day.
Lift salmon from marinade, drain (reserve marinade), and lay skin side down on a sheet of heavy foil. Trim foil to outline of fish.
Transfer fish on foil to a grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds). Cover barbecue; open vents for charcoal. Cook until salmon is opaque but still moist-looking in center of thickest part (cut to test), or 140° on a thermometer, 20 to 25 minutes. With 2 wide spatulas, transfer fish to a platter.
Return marinade to microwave oven and heat at full power until boiling, 1 to 2 minutes, stirring several times. Pour into a small bowl.
Cut fish into portions, lift from skin onto plates, and add marinade to taste.