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Put me on your Foodie ping list if you have one.

In Baltimore the only place I know to get prime beef filet is Wegmans. You're not supposed to grill a prime beef.

Here is how I do filet, it's a fantastic meal. I only sear 1 1/2 minutes because the 20 minute rest period will over cook it otherwise. I may finish it in the oven if the temp is too low and if so I use a polder thermometer, get the temp to 127 degrees and rest for 10 minutes after reaching that temp.

Rub room temperature filets on all sides with olive oil. Heat iron skillet, bottom covered with olive oil, to screaming hot.
Place filets in the skillet and sear 2 minutes on each side (time yourself so you don't overcook)
Remove skillet from heat but leave steaks in. Put a pat of butter on each steak. Let steaks sit in the skillet for 20-30 minutes under a foil tent.
Place entire skillet with steaks into a preheated 475 degree oven for 3-6 minutes depending on thickness of steaks. After baking is completed, remove steak from skillet and let it stand for 10 minutes so it can reclaim its juices.

[edit] Tips
Soften butter and add fresh garlic before placing on steaks.
Open all the windows and doors in your house. It will get smoky.
Use an iron skillet. It heats evenly and is oven safe.
Use extra virgin olive oil over other oils. If used sparingly, it won't overpower any of the tastes and actually adds more flavor.
Check meat by touch, not by cutting open, it will retain more flavor.

[edit] Warnings
The iron skillet will be really hot. Watch out!
Your house will get smoky, so ventilate.
You can eat raw steak. Ensure that the bacteria is killed by pan frying it for 20-30 seconds, there is no harmful bacteria on the inside.
Time your cooking or you will overcook the filet.
If you cut into the steak and find it too rare, return it to the hot skillet and cover with foil for one to five minutes without returning the pan to any heat source.