1. Preheat oven to 350°. Place cranberries in a small bowl; pour 1/2 cup cranberry juice over berries, and soak 10 minutes or until fruit is slightly plumped. Drain, if necessary.
2. Trim pork loin of excess fat; rinse and pat dry. Slit 1 end of pork loin with tip of a small knife to make a 1/2-inch incision. Use a sharpening steel or handle of a wooden spoon to make a tunnel inside center of pork loin. Combine cranberries and 1 tablespoon rosemary; stuff mixture down tunnel, using spoon handle to push through center. If handle isn't long enough to go all the way through, stuff from both ends. Rub pork loin with 1 tablespoon olive oil, remaining 1 tablespoon rosemary, thyme, sea salt, and pepper.
3. Heat remaining 1 tablespoon olive oil with butter in a heavy-duty roasting pan or large ovenproof skillet over medium heat. Sauté pork loin, evenly on all sides, 7 to 8 minutes or until golden brown. Add port and remaining 1 cup cranberry juice; bring to a low boil, scraping any brown bits from bottom of pan.
4. Bake at 350°, basting several times, 40 to 45 minutes or until a meat thermometer inserted into center of pork registers 150°. Remove pork from oven, and place on serving platter. Let rest, loosely covered, 10 to 15 minutes. (Pork will continue to cook.) Remove pork to serving platter.
5. Whisk together cornstarch and 1 teaspoon pan drippings. Heat remaining pan drippings over medium heat in heavy-duty roasting pan or large skillet. Whisk in cornstarch mixture. Bring to a boil, whisking constantly; boil 1 minute. Spoon over pork just before serving.