see #19
In the Adam Clayton Powell case, SCOTUS ruled that the House’s power to judge qualifications was limited to the constitutional qualifications for the office. Powell was expelled by the House, but re-elected by his constituents; the House could expel him again, a power that has no limit I know of, but could not refuse to seat him.
Similarly, the Senate’s power to judge elections would, presumably, be limited to the facts of the vote count. The courts could throw out a determination of fact without a sufficient basis, as courts sometimes do with jury verdicts.