Stir together cinnamon, salt, coriander, cumin and pepper in a shallow bowl. Pat tenderloins dry and dredge in spice mixture until evenly coated.
Heat oil in a 12-inch heavy skillet over medium-high heat until hot but not smoking. Reduce heat to medium and cook pork, turning occasionally, until meat is browned on all sides and an instant-read thermometer inserted diagonally into center of each tenderloin registers 145 degrees F, 20 to 25 minutes. Transfer pork with tongs to a cutting board and let stand 10 minutes.
Meanwhile, pour off and discard any fat from skillet, then add pomegranate juice and boil over medium-high heat until reduced to about 2/3 cup, about 3 minutes (if side of skillet begins to scorch, reduce heat to medium). Stir together cornstarch and 1 tablespoon water and whisk into juice, then boil sauce until thickened slightly, 1 to 2 minutes.
Remove from heat and add vinegar to taste. Swirl in butter until incorporated. Pour sauce through a fine-mesh sieve into a bowl and skim off any fat. Season with salt. Slice pork and serve with sauce.
This recipe has been updated and may differ from what was originally published or broadcast.