how long do you cook tuna steaks in the oven
1 Cover, and refrigerate for at least 30 minutes. 2  Preheat grill for high heat. 3  Lightly oil grill grate. 4  Cook the tuna steaks for 5 to 6 minutes, then turn and baste with the marinade. 5  Cook for an additional 5 minutes, or to desired doneness.