- In the other application's open/save dialog box, use the slash key or Cmd-Shift-G to open the "Go to folder..." option. Then in LaunchBar, use Cmd-Shift-C to send the selected item's path to the dialog box. (via this thread).
- Using an AppleScript (via this thread). (FWIW, the script doesn't work for me, at least not out of the box).
I'd love to see this functionality incorporated as on official LaunchBar feature.