Heat oven to 425 degrees F. Line a rimmed baking sheet with parchment paper. In a large bowl, combine swordfish, 2 tablespoons olive oil, lemon juice, sliced basil and ¼ teaspoon pepper.
Let stand, covered, at room temperature for 20 minutes.
Spread swordfish and its marinade in a single layer on the prepared pan. Season with salt.
Bake until cubes are just cooked through and opaque, about 5 minutes. Discard marinade and cover loosely with foil, set aside in a warm place. Meanwhile, combine cherry and grape tomatoes in a medium bowl. Season with vinegar, salt and pepper; toss to combine. Arrange the fresh tomato mixture and any accumulated liquid with the drained swordfish and on a large serving plate.
Heat remaining 2 tablespoons olive oil in small sauce pan set over medium heat.
Add the garlic slices and cook until the garlic begins to color and is very fragrant.
Pour the oil over the tomatoes while still blazing hot. Where it comes in contact with the tomatoes and basil it will cook the mixture somewhat, making a nice varied texture.