Cooking a filet mignon on an electric grill is definitely possible, even if it might be a challenge because of the thickness of the cut. You'll want to start by seasoning and marinating your steak. After two to four hours, you'll take the steak out of the refrigerator and pre-heat your grill to about four seventy-five. From here, you'll want to cook the steak for at least six minutes, flipping it once about halfway through. Check the temperature with a digital meat thermometer to determine when it is done.