In a large nonmetallic dish, whisk together the olive oil, lemon juice, and garlic. Place the tuna steaks into the mixture, turning them over to ensure they’re well coated. Cover and refrigerate for approximately 1 hour, flipping the steaks occasionally during the marinating time.
While the tuna marinates, prepare the relish: combine the fennel, tomatoes, olive oil, lemon juice, tapenade, and garlic in a bowl, stirring thoroughly until everything is evenly mixed.
Lift the tuna steaks from the marinade, setting the marinade aside for basting. Position the tuna under a preheated hot broiler, about 3 in (7 cm) from the heat source. Broil for 3–4 minutes per side, brushing with the reserved marinade once or twice during cooking.
Once cooked, sprinkle the tuna with salt and pepper, then spoon the fennel and tomato relish generously over the top. Add a finishing touch with lime wedges and delicate fennel tops, and serve alongside a crisp green salad.