Swordfish Sicilian Style is kind of a deceiving name for this dish, considering that swordfish is prepared so many different ways in Sicily. Dishes like Stuffed Swordfish Rolls  and Swordfish coated in breadcrumbs and grilled  are also very typically Sicilian just to name a couple. But, this tasty lemon, oil, garlic and white wine sauce just never fails to make me think of Sicily, and this was one first Sicilian recipes my father taught me, so it will forever be Swordfish Sicilian Style in my book.
You can prepare this on the grill also. Just cook the fish plain on the grill, and heat up a saute pan either on the side burner or the other side of the grill. When the fish is just about done transfer it to the pan, pour over the marinade, and cook for a few minutes until the sauce is reduced down.