A federal judge has sent another message to lawyers who may be tempted to use generative artificial intelligence: Always check your work.

In a decision issued on Monday, Judge Nina Y. Wang of the U.S. District Court for the District of Colorado imposed sanctions on two lawyers who represented Mike Lindell, the founder of MyPillow, who is known for spreading conspiracy theories about the 2020 presidential election.

In February, Judge Wang said, the lawyers filed a court brief in a defamation case brought against Mr. Lindell that contained “nearly 30 defective citations.” It misquoted court cases, misrepresented principles of law and, “most egregiously,” cited “cases that do not exist,” she wrote.

Judge Wang said the lawyers, Christopher I. Kachouroff and Jennifer T. DeMaster, had not explained how such errors could have ended up in the filing “absent the use of generative artificial intelligence or gross carelessness by counsel.”

She found that they had violated a federal rule that requires lawyers to certify that the claims they are making in court filings are grounded in the law. She fined them $3,000 each, calling it “the least severe sanction adequate to deter and punish defense counsel in this instance.”

Mr. Kachouroff and Ms. DeMaster did not immediately respond on Tuesday to messages seeking comment on the fines.