In a small bowl, blend the garlic oil with the basil, capers and 1 teaspoon of serrano honey balsamic. Season with spice rub, and refrigerate.
In a large, shallow dish, mix the butter olive oil with the remaining 1 tablespoon of serrano honey vinegar. Season the swordfish with more spice rub and turn the fish in the olive oil mixture. Refrigerate for 15 minutes.
Heat a grill pan or cast iron skillet over high heat until smoking and preheat the oven to 350 degrees.
Mark the swordfish steaks diagonally on one side for 1 minute, then flip and mark the other for side 1 minute. Next, flip the fish over again and rotate to the opposite diagonal to make a cross hatch pattern. Sear 1 more minute on that side. Then flip again and transfer to the oven and cook 6-8 minutes or until just barely opaque.
Transfer the steaks to plates, and drizzle each with the basil-caper vinaigrette and serve right away.