In a shallow glass dish stir together the honey, soy sauce, balsamic vinegar, ginger, garlic and olive oil. Season fish fillets with salt and pepper and place them into the dish. If the fillets have skin on them place them skin side down. Cover and refrigerate for 20 minutes to marinate.
Heat vegetable oil in a large frypan over medium-high heat. Remove fish from the dish and reserve marinade. Fry fish for 4 to 6 minutes on each side, turning only once until fish flakes easily with a fork. Remove fillets to a serving platter and keep warm.
Pour reserved marinade into the frypan and heat over medium heat until the mixture reduces to a glaze consistently. Spoon glaze over fish and serve immediately.