What powers do US judges have over an administration?

From the article:

There are no opinions of the Supreme Court on the subject, and while the courts of appeals have handled the issue many times over, they have done so in a manner calculated to avoid setting clear and general precedent. My team and I have assembled relevant cases through a wide-ranging search covering over 12,000 opinions (many of district courts) and 4,000 docket sheets. In these cases, I examined numerous unpublished opinions and orders, briefs, and other filings, and also conducted archival research and interviews. Here I offer a partial summary, focused on what’s of immediate interest for anyone litigating these issues.

1. Contempt Fines Against the Agency as an Institution?*
   [...] [T]he judiciary has carefully avoided ever getting to the point where a federal agency incurs a contempt fine[...]
2. Imprisonment of the Agency Official?
   [...] Imprisonment has occurred only twice, never for more than a few hours, and in both instances, the biggest losers proved to be the imprisoning judges, one of whom was thrown off the case for bias, while the other recused himself to avoid a similar fate. [...]
3. Fines Against the Agency Official?
   [...] In practice, courts have not much tested the viability of this maneuver as a means to circumvent federal sovereign immunity.

[...]

That contempt findings may come with no sanction does not render them powerless. [...] our research found many examples of agencies shifting toward compliance on being faced with a mere contempt motion. Agency officials and their lawyers may sometimes be willing to push the envelope on compliance, but the prospect of a contempt finding can make them back off.