Whisk miso, sugar, sake, and mirin together in medium bowl until sugar and miso are dissolved. Dip each fillet into mixture to coat evenly on all flesh sides- not skin side. Place fillets skin side down in baking dish and pour remaining miso mixture over them. Cover with plastic wrap and refrigerate for at least 6 hours or up to 24 hours.
Adjust oven rack 8 inches from broiler element and pre-heat. Place wire rack in rimmed baking sheet and cover with aluminium foil. Using your fingers, scrape miso mixture from fillets. Do not rinse. Place fillets skin side down on foil, leaving 1 inch between fillets.
Broil salmon until deeply browned and centers of fillets register 125 degrees, or 8-12 minutes, rotating sheet halfway through cooking and shielding edges of fillets with foil if necessary. Transfer to platter and garnish with lemon wedges.