In the case of Germany: a lot less, but it's not impossible.

The German equivalent to the supreme court is the Bundesverfassungsgerichtshof (BVerG, federal Constitutional Court) and in stark contrast to the highest American court, it is not an appeals court. A lower court might refer a case to the BVerG, or ask it to clarify a constitutional question, that has come up during a trial but most case don't even have a theoretical path to Karlsruhe. Political parties and NGOs may also go to directly in front of the Constitutional Court to protest the constitutionality of laws.

New justices are confirmed with a 2/3 majority which means that you need to convince roughly 30% of the opposition to vote for your candidate. That in turn leads to more moderate candidates put forward. Justices are also limited to one term of twelve years. Outside of that a justice may be removed from office by the German federal president* if 2/3 of BVerG justices vote to impeach their colleague.

So far so good. Unfortunately there are some weaknesses in the entire setup. The law responsible for needing a 2/3 majority to elect a justice can be changed with a simple majority. A right wing government could also expand the court by introducing a third senate and pack it with their appointees. But that requires them to get into power first.

German late night show Die Anstalt did a segment about that problem a while back: https://youtu.be/ljjZ6AZsmGk (Video in German)

Tldr: the highest German court is not going to stop a fascist government from doing fascism but it is also not working to put the fascists into power, the way the US supreme court is.

• Yes Germany has a president. The role is largely ceremonial though as he isn't head of government