It's what I always use.

https://www.proz.com/kudoz/spanish_to_english/education_peda...

https://www.proz.com/kudoz/spanish_to_english/law_general/29...

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Note added at 2 hrs (2018-02-25 00:51:23 GMT)
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Contentious Adminstrative Court

The Chamber of Contentious Administrative Matters is the supervising organ of public administrations in the Madrid region. It is aware of the appeals relating to the actions of local and autonomic entities, the appeals lodged against the resolutions of the courts of contentious matters, and the questions of jurisdiction amongst those courts.
Given its broad jurisdiction and functions, it is the busiest Chamber in the whole of Spain. It is made up of fifty five magistrates in active service, divided into ten sections, and it is situated in General Castaños nº 1

http://www.poderjudicial.es/cgpj/en/Judiciary/High-Courts-of...

I don't think "contentious administrative" is actually wrong. You could say "contentious administrative judicial proceedings" if you like. It is possible to have non-contentious administrative judicial proceedings (e.g. judicial review). And certainly many people use it, though I have the impression that in most cases they are simply calquing the Spanish without really thinking about why they're including "contentious" and indeed what "contencioso" actually means. I think "contentious" is redundant and unnatural here and I use just "administrative courts" and "administrative judicial proceedings". In this I agree with Rebecca Jowers:

"I know that "contentious-administrative jurisdiction" may be a good literal rendering of this expression, but I believe that the equivalent term in Anglo-American jurisdictions that have administrative courts is simply "administrative jurisdiction.""
Numerous supporting examples
https://www.proz.com/kudoz/spanish_to_english/law_contracts/...

"Some translators believe that the contencioso in recurso contencioso-administrativo has to be translated literally, but this term merely indicates that the appeal is to an administrative court (juzgado contencioso-administrativo), distinguishing it from a recurso admininistrativo, which is a (non-judicial) appeal to the administrative authorities. All appeals filed in administrative courts are by definition “administrative appeals”."
https://signsandsymptomsoftranslation.com/2017/06/30/legales...

https://www.proz.com/kudoz/spanish_to_english/law_patents_tr...


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Note added at 2 hrs (2018-02-25 01:21:41 GMT)
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Administrative courts are by definition "contencioso-administrativos"; that's why "contencioso" is redundant and (IMO) better omitted.

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Note added at 23 hrs (2018-02-25 22:16:23 GMT)
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Hi Ruth. I think a literal translation is unsuitable and would sound pretty odd. I would go with one of Rebecca's option.