He's in contempt of court. That gives a judge near limitless power, including the ability to jail someone until they comply, indefinitely if necessary.
A judge having "near limitless power," that sure sounds fancy, or scary depending how you look at it. But ok, I'll play: What's it all gonna cost if they decide to wield their limitless power. Financially and/or otherwise. Is it in or against their best interest to pursue?
Because I think a lot of judiciaries are just like companies in the sense of not wanting to draw unwanted attention, risk high costs or worse – having to deal with awkward situations at posh drinking events — think I got that last part from a movie.
It costs a judge absolutely nothing, as it's the judge's job. What does it "cost" when a judge jails a murderer or fines someone with unpaid parking tickets?
The scarier thing to consider is what does it cost not to hold this person in contempt of court? Much of society is built on the justice system being able to do its job and much of that ability is built on court orders being respected. What happens when some rich person sets a precedent of disobeying court orders without consequence?
It costs political/career opportunities and will continue to do so while the potential defendants is/knows the "establishment" of the judges area of jurisdiction.