Cooking a filet mignon on the barbecue is a classic way to prepare the meat. Filet mignon is one of the most expensive cuts of beef, and it will be very tender. Steaks are best when the are fresh and never frozen. Go to a butcher and select the filet mignon steaks yourself. Store them in the refrigerator, but bring to room temperature for at least an hour before placing on the grill.
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Add a marinade or dry rub to the filet mignon steaks. They do not require this for tenderness, but the additional flavor is appealing to some people. All filet mignon steaks really require before being put on the barbecue is pepper. You can salt the steak when it is cooked so the salt doesn't draw out the juices.
Pre-heat the grill. A hot grill will give you a perfect sear on the outside of the meat. If your grill doesn't have a temperature gauge, hold your hand two inches above the grates. If you can't keep your hand there for more than five seconds, the grill is hot enough.
Grill the steaks for three to five minutes per side for medium-rare. Don't press down on the steaks, don't puncture them for any reason, and don't move the steaks for the first two minutes that they're on the grill. Turn the steaks 90 degrees and set them down for another couple of minutes to create perfect grill marks. Flip the steaks once, then repeat the process on the other side. It may take slightly less time to cook on the second side.
Check the doneness of the steaks. Push into the steak with your finger. A rare steak will show the impression of your finger, a medium steak will give a little but there will be no impression, and a well-done steak will be firm. You can use a meat thermometer to check the doneness, but since this pierces the meat, you will lose some juices.
Let the filet mignon steaks rest. This is an important step that many people forget about. Letting steaks rest allows the juices to be redistributed through the meat so they don't spill onto your plate when you cut the meat. Leave the steaks on a platter tented with foil for two to three minutes.