In a food processor combine the olive oil, paprika, salt, cumin, pepper, and garlic until garlic is finely chopped. Add parsley and cilantro leaves, capers, rind, and juice. Pulse until herbs are coarsely chopped. Set aside and allow flavors to meld.
Turn all grill burners on high, cover, and heat the grill until very hot, about 15 minutes. Scrape the grate if it needs to be cleaned.
Brush the fish with olive oil and sprinkle generously with salt and pepper. Lightly dip a wad of paper towels in oil, and holding the paper towels with long handled tongs, wipe the cooking grate.
Grill the swordfish, uncovered, turning once over the hottest part of the grill, until steaks are streaked with grill marks, 7 to 9 minutes. Turn the heat down to medium and cook, covered, turning once, until the center is no longer translucent, 4 to 6 minutes. Serve immediately with sauce and lemon wedges.