Gather all ingredients. Preheat the oven to 400 degrees F (200 degrees C). Line a baking dish with aluminum foil. Season arctic char with sea salt, place in the prepared baking dish, and sprinkle with lime zest. Combine lime juice, olive oil, sherry, rosemary, and garlic in a food processor; pulse until garlic is finely chopped. Spread mixture over fish; season with cayenne pepper and black pepper. Bake in the preheated oven until fish flakes easily with a fork, 12 to 15 minutes, basting with pan juices about halfway through. When fish is close to being fully cooked, switch the oven to broil. Cook until the top is browned, about 2 minutes.