The individual states retain the right and responsibility to regulate run their election processes according to their own laws, where those laws do not violate the guarantee to equal protection of the law for all United States Citizens and residents. Pursuant to that power, the Legislature of each state has the power to impeach and try any official elected to the United States government that stood for election in its State for high crimes and misdemeanors. The punishment for being convicted in such a trial shall be limited to being ineligible to stand for election to any office for which the state runs elections.
Basically, if we can’t get the national level politicians to impeach the likes of Trump, we can at least hobble him badly at the state level, making his election explicitly more difficult.