The ruling said that Twitter had raised First Amendment concerns about a nondisclosure order issued over the warrant.
Twitter has been fined $350,000 by the U.S. Court of Appeals for the District of Columbia Circuit.
This comes after U.S. special counsel investigating former US president Donald Trump obtained a search warrant for his Twitter account in January and the company delayed complying.
This is according to a U.S. appeals court opinion published on Wednesday, August 9.
The U.S. Court of Appeals for the District of Columbia Circuit affirmed the federal trial judge's decision to hold Twitter, now known as X, in contempt and fine it $350,000.
The ruling said that Twitter had raised First Amendment concerns about a nondisclosure order issued over the warrant, as the company wanted to notify Trump about it.
"Under the circumstances, the court did not abuse its discretion when it ultimately held Twitter in contempt and imposed a $350,000 sanction," the ruling said.
Trump, in a post on his social media site Truth Social, said the Justice Department "secretly attacked my Twitter account, making it a point not to let me know about this major 'hit' on my civil rights."
Prosecutors will often ask judges that targets of subpoenas issued in criminal probes not be notified in order to protect their investigations, a practice the appeals court cited in Wednesday's ruling.
The opinion in court did not identify which judge held Twitter in contempt.
While Trump's tweets are viewable to the public, the company also holds non-public information on accounts like direct messages, drafts of tweets, location data and the type of device used to send tweets.
The opinion said the warrant was related to Smith's investigation into the events surrounding the Jan. 6, 2021, siege on the U.S. Capitol by supporters of Trump while he was still president.
Trump last week pleaded not guilty to an indictment that charged him with plotting to overturn his November 2020 election loss to Democrat Joe Biden. He is the front-runner for the Republican 2024 presidential nomination.