To cook filet mignon on a charcoal grill, cook the meat uncovered using medium coals, turn once while grilling, wrap in foil after transferring to a plate, and serve after five minutes. When cooking a 1-inch cut, grill for 10 to 12 minutes to achieve a medium-rare steak and 12 to 15 minutes to achieve medium-done meat. A 1 1/2-inch piece requires grilling for 15 to 19 minutes for medium rare and 18 to 23 minutes for medium done.
Another way to cook filet mignon is to use a heavy skillet that fits the size of the meat. Avoid using a skillet that is too big to avoid burning the pan juices. A very small skillet often causes the meat to steam instead of turning brown. Use paper towels to pat the steak cut dry. Preheat a heavy nonstick skillet or a skillet coated with nonstick cooking spray over medium-high heat, and put in the meat when the pan is very hot without adding liquid or covering.
Adjust the heat setting to medium, and cook for 10 to 13 minutes while turning the meat a few times if the steak cut is 1-inch thick. Cook longer for a thicker cut. Place the medium-rare or medium-done filet on a platter, cover with foil, and serve after five minutes with a topping or sauce for extra flavor.