Prepare the grill for direct cooking over high heat (450° to 550°F).
In a small bowl whisk the vinaigrette ingredients until well blended. Coat the tuna steaks on both sides with the vinaigrette and season evenly with the salt and pepper.
Brush the cooking grates clean. Grill the tuna over direct high heat, with the lid closed as much as possible, until just turning opaque throughout, about 8 minutes, turning once. Remove from the grill.
Serve warm with lemon wedges and fresh basil sprinkled on top.
