The approach I'd take is,
1. Give each judge some sort of motivation or goal that either a) the PCs can help them achieve if found innocent or b) the finding of the PCs' innocence is itself furthering the goal. For an example of a), if there are other dragon problems nearby that need dealing with; for an example of b), if some judge wants to set a precedent for allowing dragon-fighting. Corruption makes this really, really easy, but even those judges on the side of law and justice should have reasons to find the PCs innocent.
2. Make it easy for the PCs to discover these motivations or goals. Ask around, grease some palms, make some die rolls, make some promises -- and get that info into the players' hands.
3. The PCs can now use that information for leverage to persuade the judges.
Resolve it with some Charisma checks. If the players presented strong arguments, then success is innocence, and failure is light punishment, or a commuted severe punishment. If the players presented weak arguments, then success is a light punishment, or a commuted sever punishment, and failure is a severe punishment that gets reduced in exchange for "community service" (i.e. a quest). Of course if the PCs refuse the community service then the campaign shifts to a prison-break scenario...
1. Give each judge some sort of motivation or goal that either a) the PCs can help them achieve if found innocent or b) the finding of the PCs' innocence is itself furthering the goal. For an example of a), if there are other dragon problems nearby that need dealing with; for an example of b), if some judge wants to set a precedent for allowing dragon-fighting. Corruption makes this really, really easy, but even those judges on the side of law and justice should have reasons to find the PCs innocent.
2. Make it easy for the PCs to discover these motivations or goals. Ask around, grease some palms, make some die rolls, make some promises -- and get that info into the players' hands.
3. The PCs can now use that information for leverage to persuade the judges.
Resolve it with some Charisma checks. If the players presented strong arguments, then success is innocence, and failure is light punishment, or a commuted severe punishment. If the players presented weak arguments, then success is a light punishment, or a commuted sever punishment, and failure is a severe punishment that gets reduced in exchange for "community service" (i.e. a quest). Of course if the PCs refuse the community service then the campaign shifts to a prison-break scenario...