Preheat a gas or charcoal grill to high heat.
Cut each swordfish steak in half, drizzle with lemon juice and let stand for 1 minute.
Rub both sides of each steak with olive oil, salt and pepper and set aside.
Place the butter, lemon juice, lemon zest, garlic, salt and basil in a small bowl and combine well. Set aside until ready to serve.
Oil the grill grates and add the fish.
Grill the swordfish steaks until opaque throughout, 3-1/2 to 4-1/2 minutes per side. To avoid drying out the fish, do not leave unattended.
Top each piece of fish with about 1 tablespoon of the lemon-basil butter just as it comes off the grill.
Allow to rest for 2 to 3 minutes before serving.