If the international situation turns truly dire the President has the White House bomb shelter, but would probably be more likely to go to Mount Weather, Raven Rock, or aboard Air Force One or NEACP. Congress used to have a secret hideout at the Greenbrier resort in West Virginia, but not since 1992, when it was decommissioned (you can take a tour nowadays). I understand TPTB would have other priorities in the event of a national catastrophe, but has there been any planning for preserving the Supreme Court?
Probably on the list somewhere. Between saving of Garden gnomes and identifying good locations for post a post apocalyptic volleyball center.
Seriously, I think survival plans for a post war scenario would certainly include ideas on how to reconstitute a judiciary. But it will probably not be regarding specific courts. Anyway, in the immidiet aftermath, the types of judges you need are magistrates, to assist the security forces in restoring order. Not judges to decide on interpretation of law.
Yes, I recall years ago Chief Justice someone was briefed on the plan. He asked about his wife. When it was explained there was no room in the helicopter for her, he said he would refuse to evacuate. I presume they updated the plan.
Probably the Marshal’s Service will handle the Court.
Worst case, you nominate new judges and the remain 2 congressmen will ratify them.