Heat a grill pan or outdoor grill to medium.
Drizzle 2 tablespoons of oil over steaks and season all sides with salt and pepper, to taste. Put on a hot grill pan or outdoor grill. Allow the meat to cook for about 3 minutes on the first side without moving. Turn, and cook until preferred doneness is reached, another 5 minutes (just a bit more for larger cuts). Remove the steaks from the grill to a cutting board and allow to rest 5 to 7 minutes.
Meanwhile, make the sauce. In a medium saucepan over high heat, add the shallots and remaining 2 tablespoons of olive oil. Season with salt and pepper and cook until golden. Deglaze the pan with pomegranate juice, scraping up the brown bits, then stir in the cherry preserves. Bring to a boil, then reduce the heat to a simmer and cook until thick. Taste and adjust seasoning, if necessary.
Thinly slice the steak against the grain and arrange on serving plates. Serve with the cherry sauce.