Prepare the marinade by mixing olive oil, lemon juice, lemon zest, garlic, salt, and pepper in a bowl.
Place the swordfish steaks in a shallow dish and pour the marinade over them, making sure they are well coated.
Preheat your grill to medium-high heat.
Remove the swordfish from the marinade, letting excess drip off, and prepare to place them on the grill.
Grill the swordfish for about 4-5 minutes on each side, or until the fish flakes easily with a fork.
Meanwhile, in a small bowl, mix the chopped parsley and basil, then stir into the remaining marinade to create the sauce.
Once the swordfish is done, remove it from the grill and let it rest for a few minutes before serving.
Serve the grilled swordfish drizzled with the lemon herb sauce, garnished with additional fresh herbs if desired.