Beef tenderloin, and most cuts of meat for that matter, is a muscle. It likes to be relaxed when you cook it. It's more relaxed when it's warm, than freezing cold, straight from the refrigerator. It'll also cook more evenly, if it's warm. If you haven't done so, already, place your covered raw steaks on the countertop for about 30 minutes to an hour, prior to cooking them. This isn't long enough for them to pick up any bacteria, so provided your kitchen is clean ... not to worry.
Optional: Some people tie a string around the steak, at this point. They tighten it, nice and tight. They remove it, when the steak is cooked and rested. This will create a more perfectly circular or "round" steak. I like my steak to be in the shape it came in, but if you want a round steak ... go for it!
Pre-heat your oven to 450° F.
Pre-heat an oven proof sauté pan, over medium-high heat. Be sure to select a pan that is wide enough to allow for all 4 steaks, and allow space between them. They should not touch one another in the pan. This will help with heat distribution.
Season your beef with salt and freshly cracked pepper. Your beef can likely handle more salt than you might think. Really coat your beef with a nice dusting of salt (don't go crazy, though ... that's a nice piece of meat!).
Look at your steaks and make a decision about which side of each steak is the most attractive. This will be the presentation side. Make a mental note.
Add your olive oil (light olive oil, or another flavorless, high smoke point oil, is recommended) to the pan. Quickly swirl the oil around the pan. The oil should ripple, but shouldn't burn or smoke.
Once you see nice rippling of the oil, add the butter to the pan. Give the pan a quick twirl, then place the attractive "presentation side" of the steaks face DOWN in the sauté pan.
Allow the steaks to simply sit and sear in the pan for about 3 minutes. Try not to move them around, poke them or swirl the pan around. I know it's tempting, but let the surface of the steak get a nice caramelization from the bottom of the pan. If there isn't a scorching or "frying" sound, then turn the heat up on the stove. If the pan isn't hot enough, the beef will "steam" rather than "sear". This will great a gray lump of meat and won't retain as much of the juices. You must sear the presentation side of the beef, to get a nice brown color.
Once the presentation side has a nice deep sear on it, flip each steak in the pan.
Let the steak sear for 1 minute.
Place the entire pan in the oven for about 5 minutes.
Poke the fleshy lump at the base of your palm, where it intersects with your thumb. Press this portion of your palm with your opposing index finger and make a mental note about the "spring" it gives back, when you poke it.
Open the oven and poke the smallest steak. It should "spring", or give back, in a fashion very similar to the poking of your palm (poke the very center, or the hardest part of your palm, for a medium well). Alternately, use a meat thermometer, in the thickest part of the steak (this makes a hole in the steak, allowing some juices to leak out, but ... sometimes you gotta do what you gotta do). When the internal temperature of the smallest steak is 120° F remove it from the oven. Normally, the steaks are all approximately the same size, so removing the entire pan is appropriate.
Remove the steaks from the pan and place to the side, in a warm location, on a plate. They will continue to (carryover) cook, on their own. This should bring them up to a nice medium-rare, while also allowing the muscle to relax, again, and the juices to settle within the meat. It's at this point I often hear "But I want my steak to be HOT!" Yes, you can serve it fresh out of the oven, and it will be hotter on the surface, but it will also be cooler in the center and more juice will bleed out, when cut. It's also true that more flavor exists closer to body temperature. Extreme heats and colds loose deaden some of the flavor. A nice warm, relaxed steak is the way to go.
Final suggestion: At this point, the pan has nice little bits of beefy goodness (known as "fond") stuck to the bottom of the pan. Throw some mushrooms, capers, garlic and black pepper in that pan! This will help pick up the fond. Then, hit the pan with a little red wine and some cream. If any juices have leaked out of the steaks, pour those juices into the pan. Cook for a moment, until the creamed mushrooms have thickened , a bit. Place the mushrooms on a plate, then perhaps some grilled asparagus and top it with a steak. Enjoy!