1) Prepare the griddle (medium-high heat).
2) Whisk the oil, mint, lemon juice, basil, and garlic in a medium bowl to blend. Season the lemon and olive oil mixture with salt and pepper, to taste.
3) Brush the swordfish steaks with two tablespoons of the lemon and olive oil mixture. Grill the steaks until just cooked through, about three minutes per side (depending on thickness of steaks). Transfer the steaks to plates. Spoon the remaining sauce over and serve.