Using a sharp knife, score each fish on one side by making 2 parallel diagonal incisions about 1¼ in (3 cm) apart. Turn the fish over and make 2 more parallel incisions on the diagonal. Make the cuts deep enough to almost touch the bone.
Combine the water, salt, saké, soy sauce, mirin and sugar and bring to a boil in a deep skillet. Add the ginger and co