Preheat an outdoor grill for high heat, and lightly oil the grate. Rub the New York steaks on both sides with the Worcestershire sauce, then season to taste with salt and pepper.
Cook the steaks on the preheated grill until they are beginning to firm, and are hot and slightly pink in the center, 6 to 7 minutes per side. An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C). Once the steaks are done, cover them with two layers of aluminum foil, and allow to rest in a warm area for 10 minutes.
While the steaks are cooking, prepare the cherry sauce by bringing the red wine to a boil in a saucepan over medium-high heat; boil for 5 minutes. Stir in the cherries, sugar, and vanilla extract. Return to a boil, then reduce heat to medium, and simmer until the cherries are tender, 5 to 7 minutes. Dissolve the cornstarch in the water, then stir into the simmering cherry sauce. Cook for a few minutes until the cherry sauce thickens.
