According to Wikipedia, the same cut of beef can be called Chateaubriand, tournedos, filet de bouef (French), Medallians, Tenderloin Steak (USA), or Fillet Steak (UK and Ireland).

The two secrets to this simple recipe are (1) a grill pan, and (2) RESISTING the temptation to turn the steak too frequently. (A grill pan is a large saute pan that has raised grill ridges.) I've grilled filet mignon before, and it's terrific, but this is one of the few cases where I actually prefer the grill pan -- it sears with a moister method than grilling -- it cooks nearer to its own juices, making it less likely to dry out.

Place the pan over medium high heat, and allow to come up to temperature (approximately 4-5 minutes). Add 1-2 tablespoons of vegetable oil and tilt it around to cover the pan. Slice medallions in very consistent-thickeness slices, approximately 1 inch thick. Cover with ample ground course salt and pepper.

Place tournedos (fillets), putting them down away from you, one by one, into the pan. DO NOT DISTURB them for 3 minutes. Lift with tongs and flip. Wait another 2-3 minutes. Rotate 45 degrees, and sear for another 2 minutes. Flip again to complete the grill marks, and cook another 1-2 minutes. I like my steaks medium, and I carefully watch the color on the outside -- remove them from the grill pan when there is still a faint pink line in the center. Tonight I found that cooking time for me was about 5-6 minutes total.