The only relevant case heard by SCOTUS is Nixon v. US, 506 U.S. 224, where a federal judge was tried and convicted for actual crimes, but would not resign his position so continued to draw his salary. The key legal question was whether the matter is "justiciable" (meaning, not a political matter but a legal matter). Nixon's argument was that Senate Rule XI violates the Impeachment Trial Clause, and the court held that the question (more specifically what it means to "try") is nonjusticiable. White & Blackmun, and Souter, wrote concurring opinions (which might be called on in a subsequent impeachment case) that reminds the reader (and future court) what was not part of the holding of the court, and what might therefore allow future impeachment review. White writes
The Court is of the view that the Constitution forbids us even to
consider his contention. I find no such prohibition and would
therefore reach the merits of the claim. I concur in the judgment
because the Senate fulfilled its constitutional obligation to "try"
petitioner.
He observes that
the Senate has very wide discretion in specifying impeachment trial
procedures and because it is extremely unlikely that the Senate would
abuse its discretion and insist on a procedure that could not be
deemed a trial by reasonable judges.
But,
I would prefer not to announce an unreviewable discretion in the
Senate to ignore completely the constitutional direction to "try"
impeachment cases. When asked at oral argument whether that direction
would be satisfied if, after a House vote to impeach, the Senate,
without any procedure whatsoever, unanimously found the accused guilty
of being "a bad guy," counsel for the United States answered that the
Government's theory "leads me to answer that question yes." Tr. of
Oral Arg. 51. Especially in light of this advice from the Solicitor
General, I would not issue an invitation to the Senate to find an
excuse, in the name of other pressing business, to be dismissive of
its critical role in the impeachment process.
Souter in his opinion states that
One can, nevertheless, envision different and unusual circumstances
that might justify a more searching review of impeachment proceedings.
If the Senate were to act in a manner seriously threatening the
integrity of its results, convicting, say, upon a coin toss, or upon a
summary determination that an officer of the United States was simply"
'a bad guy,'", judicial interference might well be appropriate. In
such circumstances, the Senate's action might be so far beyond the
scope of its constitutional authority, and the consequent impact on
the Republic so great, as to merit a judicial response despite the
prudential concerns that would ordinarily counsel silence.
In other words, review of an impeachment is largely but not entirely off the table, at least until SCOTUS declares that impeachments are completely unreviewable, no matter what, period (unlikely to ever happen).
