Trim any fat and silverskin (silver colored connective tissue) from the tenderloin. Mix 2 tablespoons olive oil, orange juice, lime juice, garlic, cilantro, cumin, oregano, salt, and red pepper flakes together in a bowl. Pour about half of the marinade into a one-gallon resealable plastic bag. Add the pork to the bag, close and refrigerate for at least 30 minutes or up to 24 hours. Pour the other half of the marinade into a small saucepan to use for the sauce.
When ready to cook, preheat the oven to 400°F. Heat the remaining tablespoon of oil in a large oven-safe skillet (cast iron works well) over medium high heat. Remove the pork from the marinade and add it to the pan. Sear the tenderloin in the pan, turning it every couple of minutes, until it’s nicely browned on all sides.
Place the skillet in the oven and cook about 15-18 minutes, or until the internal temperature of the pork measures 145°F on a meat thermometer. Alternatively, the tenderloin can be cooked on an outdoor grill. Remove the tenderloin from the oven and let it rest on a cutting board for 5-10 minutes.
While the pork is resting, pour any pan drippings into the saucepan with the reserved marinade. Simmer on the stove for a few minutes until thickened slightly. Pour the sauce in a bowl.
Cut the pork into ½-inch slices and arrange on a platter. Serve the mojo sauce on the side.