Combine mayonnaise, lemon juice, garlic, basil, thyme, tarragon and dill in a small bowl. Season with salt and pepper. (Herb sauce can be prepared 2 days ahead. Cover and refrigerate.)
Butter 8-inch square baking dish. Spread each side of swordfish steaks with 1 tablespoon herb sauce. Place in prepared dish and chill 30 minutes.
Preheat oven to 400°F. Pour wine over swordfish. Bake until fish is just cooked through, about 17 minutes. Transfer to plates. Serve, passing remaining herb sauce separately.
