Light a grill. In a small bowl, blend the butter with the basil, capers and 1 teaspoon of the lemon juice. Season with salt and pepper, and refrigerate.
In a large, shallow dish, mix the olive oil with the remaining 1 tablespoon of lemon juice. Season the swordfish with salt and pepper and turn the fish in the olive oil mixture. Refrigerate for 15 minutes.
Grill the swordfish steaks over a hot fire until nicely charred on the outside and just cooked within, about 4 minutes per side. Transfer the steaks to plates, top each with a dollop of basil-caper butter and serve right away.