In a small saucepan over medium heat, add and mix the lime juice, brown sugar, vinegar, and soy sauce until thickened. (Approx. 5 minutes)
Spray the bottom of a casserole dish with cooking spray and prepare the black cod inside. Pour the thickened sauce over the fish and arrange the halved tomatoes around the fish.
Cover the pan with an oven-safe lid and cook for approximately 10 minutes, or until the fish flakes easily with a fork.