Preheat the grill to medium-high heat.
In a mixing bowl, toss the halved cherry tomatoes with olive oil, balsamic vinegar, salt, and pepper. Spread them on a baking sheet and roast in the oven at 400°F for about 15 minutes, or until they are blistered and soft.
While the tomatoes are roasting, season the cod fillets with salt and pepper. Place them on the grill and cook for about 4-5 minutes on each side, or until the fish flakes easily with a fork.
In a small bowl, combine the sour cream, dill, lemon juice, and minced garlic. Mix well and season with salt and pepper to taste.
Once the cod is cooked and the tomatoes are roasted, plate the cod fillets and top them with the roasted tomatoes. Drizzle the creamy dill sauce over the top.
Serve immediately.