Place the pork tenderloin in a plastic, sealable bag. Squeeze juice of oranges and lime into measuring cup. Combine remaining marinade ingredients in measuring cup and stir to combine. Pour over the tenderloin and seal bag. Marinate overnight in the refrigerator.
Preheat an outdoor grill or preheat oven to 350°F.
Remove pork tenderloin from marinade and pat dry. Brush olive oil onto grill and over meat for extra flavor. Reserve marinade. Grill tenderloin about 35 minutes to 40 minutes over medium heat. Or roast for 45 minutes. Allow meat to sit about 10 minutes before cutting into two inch serving pieces.
While meat is grilling, bring reserve marinade to a boil in a small saucepan, them lower the heat and gently simmer until it is reduced to about 2 tablespoons. Stir occasionally. Drizzle a small amount of marinade over each piece of meat.