Whisk Marsala wine, ketchup, garlic, kosher salt, rosemary, and black pepper together in a large glass or ceramic bowl. Add skirt steak and turn to evenly coat. Cover the bowl with plastic wrap, and marinate in the refrigerator, 8 hours to overnight.
Preheat an outdoor grill for high heat, and lightly oil the grate.
Remove steak from marinade, shake off excess, and discard marinade.
Cook steak on the preheated grill until meat shines, 3 to 4 minutes per side. An instant-read thermometer inserted into the center should read 130 degrees F (54 degrees C). Transfer meat to a plate and let rest at least 5 minutes before slicing against the grain.