Fred Barbash has this analysis in the Washington Post of whether courts can entertain challenges to ballot access for possibly ineligible presidential candidates. He finds that such a challenge cannot work in federal courts, but might work in state courts. But the only surefire way to get into court would be for an elections administrator to bar the candidate first, and then of course the candidate could sue in either state or federal court.
Ballot Access News
Edited By Richard Winger
I think Professor Tokaji is correct in his Michigan Law Review article (2008), which is relied upon in the news account. About the only way to go about it judicially is to have a state administrator remove a candidate, and then have the candidate challenge the removal. But then I am not so sure that state court is better than federal court. If filed in state court, even, it could be removed to federal court. The candidate would there plainly have Article III standing, and the political question doctrine would not appear to be an obstacle (if the candidate has not even been allowed to participate in the election in the first instance).