Prep the fish. Place the swordfish in a large bowl or a resealable bag.
Make the marinade. In a small mixing bowl, combine the olive oil, garlic, soy sauce, lemon juice, red wine vinegar, rosemary, thyme, salt, and pepper; whisk until well incorporated.
Combine and marinate. Pour the marinade over the swordfish and seal the bag (or cover the bowl). Let the fish marinate at room temperature for 15 to 30 minutes, or place it in the fridge for up to 8 hours.
Prepare to grill. Remove the swordfish from the bag, discard the marinade, and preheat your grill to medium-high heat.
Grill. Transfer the fish steaks to the grill and cook them for 5 to 7 minutes per side or until cooked through and opaque. Swordfish is cooked through when its internal temperature registers at 145˚F.
Finish and serve. Remove from the grill and let it rest for 5 minutes. Garnish with parsley and serve with lemon wedges.