I'm going to cook a couple filet mignon steaks. I want to sear them on the stove and then finish them in the oven with butter.

Thank you Julie! I'm going but the kosher salt on them first and draw out that liquid for a better sear. I will do that for about 30 mins and rinse it and cook them.

Hi there...I usually sear on high heat in a cast iron pan on the cook top (don't foget lots of kosher salt and fresh ground pepper), then I just put entire pan in a preheated 400 degree for about 5-7 minutes.
Perfect every time.

Thank you both so much!

Set the oven to 225 degrees. If you have a good feel for the "poke," it's quite accurate. Otherwise, as ChrisBird suggests, use a thermometer. For a doneness of not more than medium, remove the steaks from the oven when you get a reading of about 130, then cover them with a piece of foil and a kitchen towel and let them rest for about 7 minutes.

There is no precise time. It depends on how done you want them, how thick t hey are, how long they were seared, the temperature they were at when you put them in the pan to , and the oven temperature. Best to use a probe thermometer unless you are confident you can determine desired doneness by touch.
Sorry to be less helpful than you want. There are just too many variables.