Combine the mirin and sake in the smallest saucepan you have and bring to a boil over high heat. Boil 20 seconds, taking care not to boil off much of the liquid, then turn the heat to low and stir in the miso and the sugar. Whisk over medium heat without letting the mixture boil until the sugar has dissolved. Remove from the heat and whisk in the sesame oil. Allow to cool. Transfer to a wide glass or stainless steel bowl or baking dish.
Pat the fish fillets dry and brush or rub on both sides with the marinade, then place them in the baking dish and turn them over a few times in the marinade remaining in the dish. Cover with plastic wrap and marinate for 2 to 3 hours, or for up to a day.
Light the broiler or prepare a grill. Line a sheet pan with foil and oil the foil. Tap each fillet against the sides of the bowl or dish so excess marinade will slide off. Place skin side up on the baking sheet if broiling.
Place the fish skin side down on the grill, or skin side up under the broiler, about 6 inches from the heat. Broil or grill for 2 to 3 minutes on each side, until the surface browns and blackens in spots. If necessary (this will depend on the thickness of the fillets) finish in a 400-degree oven, for about 5 minutes, until the fish is opaque and can be pulled apart easily with a fork.