1. Preheat grill to 350° to 400° (medium-high) heat. Remove silver skin from tenderloins, leaving a thin layer of fat. Brush tenderloins with oil, and rub with seasoning and salt.
2. Grill tenderloins, covered with grill lid, 10 minutes on each side or until a meat thermometer inserted into thickest portion registers 155°. Remove from grill, and let stand 10 minutes.
3. Meanwhile, whisk together blackberry preserves and next 4 ingredients in a small saucepan, and cook over low heat, whisking constantly, 5 minutes or until thoroughly heated.
4. Cut pork diagonally into thin slices, and arrange on a serving platter; drizzle with warm sauce.