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