SAN FRANCISCO—If a company wants to sue a former board member for being disloyal and infringing company patents, it’s probably going to have to do so in separate courts.

That’s the takeaway from the U.S. Court of Appeals for the Federal Circuit’s decision Thursday in AngioScore v. TriReme Medical. The appellate court wiped out a medical device maker’s $20 million verdict for state-law fiduciary duty claims, saying they never should have been tied to a patent infringement suit brought in federal court.