Add the tomatoes, jalapeño, onions, cilantro and lime juice to a bowl and mix to combine. Add 2 tablespoons olive oil and season with salt and pepper. Let sit at room temperature for at least an hour for all the flavors to come together.
Set up your grill for indirect heat. If using a charcoal grill, build the coals on one side only. If using a gas grill, heat one side only. Drizzle the swordfish with olive oil and sprinkle with salt and pepper on both sides. Place on the direct-heat side of the grill and cook until nicely charred, 2 to 3 minutes per side. Move to the indirect-heat side of the grill, close the lid and cook until cooked through, another 3 to 4 minutes. Remove from the grill to rest, about 5 minutes. Serve the swordfish with the salsa spooned over the top.
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