Heat the olive oil in a large saute pan over medium heat. Add the tomatoes and season with a pinch of salt and pepper. Cook the tomatoes until they pop and become soft, about 20 minutes. Add the garlic and cook for a minute more. Remove the pan from the heat and stir in the basil.
Meanwhile, season each side of the fish with salt and pepper. Place the swordfish on the grill, cook for 5 minutes, then use tongs to flip the fish and cook for 5 minutes on the other side.
Remove the swordfish from the grill. Divide between plates and top with the tomato and basil mixture.