Mix together the orange juice, lime juice, chopped oregano, thyme leaves, minced garlic, salt, and olive oil in a large glass bowl.
Place the pork tenderloins in a zipper bag and add half of the marinade. Seal the bag and marinate at least overnight.
Place the remaining marinade in the refrigerator.
When you are ready to cook the pork, place a large skillet in an oven and preheat to 375°F.
While the pan is preheating, remove the marinating pork tenderloin and the extra marinade. Set the extra marinade aside.
Place the pork tenderloins in the preheated pan and return the pan to the oven.
Cook for 4 minutes and turn the pork every 3 minutes after that, until all the sides are seared.
Strain the remaining marinade used for the pork and discard the strained herbs and garlic, reserving the liquid. (If you do not strain the marinade, the herbs will burn and the sauce will become bitter.)
After the second turn, baste with 1/2 cup of the strained marinade, coating the tenderloins well.
As the pork cooks and the marinade is reduced, continue to baste the tenderloin to create a caramelized glaze on the pork.
It should take 20 – 25 minutes to reach an internal temperature of 140°F. As the pork is finishing, add the remaining marinade to create a syrupy sauce.
Remove the pork from the oven and place on a cutting board to rest for 5 minutes before carving.
While the pork is resting, add the other half of the marinade to the skillet, place the skillet over medium high heat, and bring the marinade to a boil.
Reduce the heat to a simmer and reduce the sauce by half.
Add the butter and whisk until smooth.
Serve the sauce over the sliced pork.