In an unusual case, relatives sought to appeal on behalf of the late Abdel Baset al-Megrahi, a former Libyan intelligence officer.
Some of the victims' families believe al-Megrahi was not responsible for the bomb that exploded aboard a New York-bound Boeing 747 in 1988, killing 270 people.
Usually only a convict's executors or family can mount a posthumous appeal, and judges in Edinburgh ruled Friday that the law does not "allow victims or relatives of victims to be direct participants in criminal proceedings."