Mash the butter ingredients together. Roll into a log in plastic wrap and chill until firm, or just keep it soft in a bowl.
Pat the swordfish dry, brush with olive oil and season well. Let it sit at room temperature 15 minutes.
Heat the grill to high and oil the grates. Grill 4–5 minutes per side, rotating 45° halfway through each side for crosshatch marks, until just opaque in the center. Swordfish dries out fast — pull it as soon as it's cooked through.
Top each steak with a thick slice of the butter so it melts over the fish. Serve with lemon wedges.
