Prepare an outdoor grill with hot coals or heat a gas grill to high.
In a small bowl, whisk together soy sauce, wine, lime juice, ginger, mustard, garlic, sesame oil and black pepper. Place in a shallow dish with the tuna steaks and turn to coat. Marinate 15 minutes.
Remove tuna from the marinade and shake off excess. Reserve marinade.
Grill tuna steaks for about 2 minutes on each side for medium rare or more as desired. Remove to a warm platter.
While fish is grilling, place reserved marinade in a small saucepan and boil for 5 minutes. Allow to cool slightly.
Toss salad greens with marinade and serve with the tuna.