1. Prepare grill to medium heat.
2. Heat a medium saucepan over medium heat. Coat pan with cooking spray. Add shallots to pan; cook 3 minutes or until tender, stirring occasionally. Add blackberries, sage, and broth; bring to a boil. Reduce heat, and simmer 20 minutes or until blackberries break down. Press blackberry mixture through a fine sieve over a bowl; discard solids. Return liquid to pan. Stir in vinegar and sugar; bring to a boil. Cook until reduced to 3/4 cup (about 9 minutes); remove from heat. Stir in butter and 1/4 teaspoon salt, stirring until butter melts. Keep warm.
3. Sprinkle remaining 1/2 teaspoon salt and pepper over pork. Place pork on grill rack coated with cooking spray; cover and grill 20 minutes or until a thermometer registers 155° (slightly pink), turning pork occasionally. Let stand 10 minutes. Cut crosswise into 1/4-inch-thick slices. Serve with blackberry sauce; garnish with sage sprigs, if desired.