Heat the oven to 400°F. Pat the pork tenderloin dry, then season all over with the kosher salt and black pepper.
Heat the olive oil in a large ovenproof skillet over medium-high until shimmering. Add the meat and sear on all sides until deeply browned, 6–8 minutes total.
Transfer the skillet to the oven and roast until the thickest part registers 140–145°F on an instant-read thermometer, 12–15 minutes. Transfer to a plate and tent loosely to rest.
Set the skillet over medium heat and add the shallot to the pan drippings; cook, stirring, until translucent and fragrant, 1–2 minutes.
Pour in the ruby port, bring to a boil, and scrape up any browned bits; reduce by about half, 2–3 minutes.
Stir in the dried tart cherries, the low-sodium chicken stock, and the fresh thyme. Simmer until the cherries plump and the liquid reduces to a glossy sauce that lightly coats a spoon, 5–7 minutes.
Off the heat, stir in the balsamic vinegar and the unsalted butter until melted and the sauce is emulsified.
Slice into 1/2-inch medallions and spoon the warm cherry sauce over to serve.