Cut tenderloin into 8 1 1/4-inch-thick medallions. In a small bowl, combine flour, 1/2 tsp. salt and 1/4 tsp. pepper. Dredge medallions in flour mixture and shake off any excess.
In a large skillet over medium-high heat, warm butter and oil until butter melts. Cook medallions, in batches if necessary, until lightly browned, about 4 minutes per side. Remove to a platter and cover loosely with foil to keep warm.
Pour off any fat remaining in skillet. Return skillet to heat and pour in broth and cider. Increase heat to high and bring to a boil. Boil rapidly, stirring with a wooden spoon to pick up browned bits on bottom of skillet, until liquid is reduced by half, about 5 minutes.
Return medallions to skillet, reduce heat to medium and cook, turning, until sauce is syrupy and medallions are cooked through, about 5 minutes.