Mix together the orange juice, lime juice, chopped parsley, chopped oregano, thyme leaves, minced garlic, salt and olive oil in a large glass bowl. (This makes approximately 3 cups.).
Place the pork tenderloins in a zipper bag and add two cups 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 non-stick skillet in an oven and preheat to 450°F.
While the pan is preheating, remove the marinating pork tenderloin and the extra marinade. Strain the cup of extra marinade in a small sauce pan over high heat and bring to a boil. Reduce the heat to medium and simmer gently to reduce by half.
Remove the pork tenderloins and place them on a plate. Strain the remaining marinade and discard the strained herbs and garlic, reserving the liquid.
Place the pork tenderloins in the preheated pan and return the pan to the oven. Cook for about 4 minutes and turn the pork every 3 minutes after that, until all the sides are seared. 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 with 1/4 to 1/2 cup at a time to create a caramelized glaze on the pork. It should take 20 – 25 minutes to reach an internal temperature of 160°F As the pork is finishing, add the remaining marinade to create a syrupy sauce.
Remove the pork from the oven and let rest on the counter for about 3 minutes before carving. Serve with the reduced sauce from the pan.