Heat oven to 400 degrees. Arrange fillets in the center of parchment rectangles. Season with salt and pepper and top with tomatoes. Drizzle with oil.
Fold parchment closed and transfer to a rimmed baking sheet.
Bake until fish is cooked through, 12 to 14 minutes. Top with basil before serving.
TIP For foolproof folding, arrange fillet in the center of a 12-by-16-inch parchment rectangle. Join long sides together and make a few ¼-inch folds to seal. Fold ends (like you’re wrapping a gift) and tuck underneath.