Should an Objectivist judge vindicate an individual's right at the expense of the objective meaning of a law?

The proper response depends on how corrupt the legal system has become. If the government has become fundamentally hostile to individual rights, as was the case in Atlas Shrugged (or in modern totalitarian states like Nazi Germany or North Korea), then withdrawing sanction and support from the system as a whole is an appropriate response. This applies to judges as much as to any other profession under a totalitarian regime.

The more interesting question is the mixed case, as in the United States today. If we take the view that an Objectivist cannot morally act as a judge in a mixed economy due to the risk of having to enforce unjust laws, we cede control of the government to those unconcerned with the justice of the laws they enforce. While every individual has their own limit, I think there would be great value in a judge who explicitly upholds the rule of law by enforcing unjust laws while simultaneously explaining the injustice of the law being applied. Mixed systems survive in part by never letting the nature of what they are doing become clear. An Objectivist judge who made clear the implications of consistent application of unjust laws might well be a great force for good in the culture. It is also worth noting that there are choices other than 'apply the law' and 'resign' -- for example, a judge might recuse himself from a particular case if he found himself unable to render objective judgment on it under the law as written.

An Objectivist judge should not subvert the rule of law by acting as though a law does not mean what it objectively does mean. That would be a form of usurpation, and accepting it as a principle by which judges in general should act would replace the rule of law with rule from the bench. Tara Smith's article "Why Originalism Won't Die: Common Mistakes in Competing Theories of Judicial Interpretation" touches on some of these issues, particularly in Section VII.

If we are talking about an Objectivist judge, he should resign -- if the law truly leaves him no legally defensible latitude. What else is a judge supposed to do if a legislature says that something shall be illegal and the judge disagrees? If the judge fails to uphold the legislature's will, he is likely to be removed from office anyway. If he wants to refuse to enforce a bad law and has no choice about it if he remains on the bench, then he should resign from the bench in protest. In fact, failure to do so could be a form of sanctioning evil.

There is actually a fictional "precedent" for this in Atlas Shrugged, in the character of Judge Naragansett.

Before resigning, however, any Objectivist judge would do well to examine closely whether or not the law truly allows him no leeway in interpretation and application.