Mix the sesame oil, tamari sauce/balsamic vinegar, ginger, garlic, onion, and lime juice. Pour this over the tuna steaks in a glass dish, cover, and marinate for 10 minutes (up to 2 hours only) in the refrigerator.
Bring the grill to medium-high heat. Remove tuna from the marinade and place on the grill for 2-3 minutes on each side. Remove and let sit for a minute before serving.