Preheat oven to 400 degrees F. If desired and to cook evenly, tie off pork tenderloin at 1 1/2″ intervals.
Heat an ovenproof skillet over medium-high heat. Add a tablespoon or two of oil. Brown pork tenderloin well on all sides.
While pork is cooking, combine preserves, soy sauce, lime or vinegar, and garlic in a microwave-safe bowl. Microwave at high in 30-second intervals, or until the preserves are just melted. Add the salt and a dash or two of hot sauce.
Brush the tenderloin with the preserve mixtures and place in oven for about 15 to 20 minutes. Brush the preserve mixture on again, about halfway through cooking time and again when nearly done. Watch the residue at the bottom of the pan so it doesn’t burn, adding a little water if needed.
Remove from oven when a thermometer registers 145°F to 160°F, depending on your preference. Remove to a cutting board or platter and let stand several minutes. Add another tablespoon or so of the preserves to the juices in the pan and pour over the pork if desired. Cut pork crosswise into slices. Sprinkle evenly with salt and pepper.
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