1Place blackberries, lime juice and honey in blender. Cover and blend on medium speed about 45 seconds, stopping blender occasionally to scrape sides, until smooth. Strain sauce. Cover and refrigerate until serving.
2Set oven control to broil. Place peach halves, cut sides up, on large piece of heavy-duty alumium foil. Sprinkle with brown sugar, cinnamon and liqueur. Fold foil over peaches and seal.
3Broil foil packet with top about 4 inches from heat about 15 minutes or until peaches are heated through. Serve hot with blackberry sauce. Garnish with additional blackberries.