Preheat grill; grease rack.
Prepare Tomato-Basil-Butter Sauce.
Rinse tuna; pat dry with paper towels.
Season rinsed tuna with salt and pepper.
Brush with olive oil.
Place on greased rack about 4 inches above hot coals or high heat.
Grill 1 to 2 minutes on each side, turning once.
Do not cook well-done.
Fish should remain rare and red in center.