I saw a segment on how to grill beef on one of the Food Network shows a few weeks ago. Here are my tips.
Okay, I am assuming that you are in Florida and that you will actually be 'grilling' like on an outdoor gas grill.
Here are the DO's
1. Start with the meat at room temperature. Let the meat sit out for little while so that it is not cold. If it is cold, then this is why grilling it long enough to heat the inside will often 'char' the outside. Let the meat reach room temperature.
Grill for as short amount of time on a medium-hot (not warm and not red-hot) grill. If the meat is already room temperature, this will 'braise' in the juices, so that they are retained inside, and the middle will indeed become heated before it becomes too charred. Too me, it is perfectly fine for a Filet to still be pink inside.
2. With a Filet, I would recommend a bacon-wrap. This is to protect from charring more than it is to add any flavor. Filet does not have a fatty outside layer.
3. With Filet, you want to really focus on the delicious flavor of this top quality meat. I would use a little salt, maybe just a little sprinkle of garlic, and some people would use a little paperika.
Now the DON'Ts
1. Do not cook too long over too low of a temperature. This is a prime cut of meat, not a chuck-roast to be slow-cooked. The longer it is cooked, the more rubbery it might become.
2. Do not use a knife to cut slits across the surface, poke holes, or pound this meat. The less it is handled the better. You do not want to breach the surface in any way, which would just be a way for all the juices to run out as it is cooking.
3. Do not cut and serve instantaneously right off the grill. Place on a serving dish for a few moments (covered) to let the meat 'cure'. If cut into while it is still super steaming hot, this just lets the meat steam-dry. You don't want to let it get cold, but just a few minutes of 'curing' can make all the difference. (This applies to any kind of roasted meat.... anything from meatloaf to turkey.)
Good Luck on preparing a wonderful meal !