Impeachment in South Korea And Political Prosecutions In Spain

In South Korea, the impeachments are tried not by an upper house of a legislature, but by the Constitutional Court, which must convicted by a six votes out of nine in the case of the President (it currently has three vacancies, so a unanimous vote is required) and by five votes out of nine in other cases. Specifically:

For passage, the [impeachment] motion must receive the support of a two-thirds majority if it concerns the president and a simple majority for any other office. Once the impeachment motion passes the National Assembly, the Constitutional Court adjudicates the impeachment, and until the Constitutional Court renders a decision, the impeached official is suspended from office and unable to exercise power.

The person facing impeachment is suspended from office once the National Assembly votes to impeach.

According to Article 65 Clause 1, if the President, Prime Minister, or other state council members violate the Constitution or other laws of official duty, the National Assembly can impeach them.

Clause 2 states the impeachment bill must be proposed by one third and approved by a majority of members of the National Assembly for passage.

By the Constitutional Court Act, the Constitutional Court must make a final decision within 180 days after it receives any case for adjudication, including impeachment cases.

From here.

While this system potentially has its own problems, it is better than the partisan vote in the Senate that is used in the U.S.

This is why many countries follow this practice:

Constitutions in 9 democracies give a court—often the country's constitutional court—the power to begin an impeachment; another 61 constitutions place the court at the end of the process.

Indeed, while bicameral national legislatures aren't uncommon, in many countries, unlike the U.S., they aren't co-equal. The lower house can overrule objections of the upper house, for example, in the case of the U.K. House of Lords, and in the case of the Canadian Senate. 

Meanwhile, "in Spain, possible criminal cases against protected people (aforados) are sent immediately to a higher tribunal (Tribunal Suprempo) in order to minimize rogue judges moving baseless cases forward. If that tribunal does actually charge the aforado, then it asks the Parliament to remove the immunity, and the affected person has the opportunity to make his case before the Parliament and try to convince it that immunity should not be lifted because the case is just a political witch hunt."

I'm not a huge fan of Spain's approach, but it does at least, insure that a politician's immunity is not absolute.