Whisk together first 5 ingredients in a small bowl; divide marinade in half, and set one half aside. Pour other half of marinade into a large, heavy-duty zip-top plastic bag; add tuna. Seal; chill up to 2 hours.
Remove tuna from marinade, discarding marinade. Grill tuna, covered with grill lid, over medium-high heat (350º to 400º) 1 to 3 minutes on each side or to desired degree of doneness.
Place reserved marinade in a small saucepan; bring to a boil. Boil 4 minutes or until reduced to 1/4 cup. Spoon glaze over tuna steaks.