In a medium-size, heavy saucepan, combine the port, chicken broth, figs, rosemary, cinnamon, and honey. Boil over medium-high heat until reduced by half, about 30 minutes. Discard the rosemary sprigs and cinnamon sticks (some of the rosemary leaves will remain in the port mixture). Transfer the port mixture to a blender and purée until smooth. Blend in the butter, salt, and pepper. (The sauce can be made 1 day ahead. Cover and refrigerate. Rewarm over medium heat before using.)