Paul Chambers was flanked by Fry and comedian Al Murray as three judges, headed by the Lord Chief Justice, Lord Judge, started a review of his case at the High Court.
The accountant was fined £385 and ordered to pay £600 costs at Doncaster Magistrates' Court in May 2010 after being convicted of sending ''a message of a menacing character'', contrary to provisions of the 2003 Communications Act,
He said he sent the tweet to his 600 followers in a moment of frustration after Robin Hood Airport in South Yorkshire was closed by snow in January 2010, and never thought anyone would take his ''silly joke'' seriously.
It read: ''Crap! Robin Hood Airport is closed. You've got a week and a bit to get your shit together, otherwise I'm blowing the airport sky high!''
But, in November 2010, Crown Court judge Jacqueline Davies, sitting with two magistrates, dismissed his appeal, saying that the electronic communication was ''clearly menacing'' and that airport staff were sufficiently concerned to report it.
Opening a new bid to overturn his conviction and sentence, John Cooper QC told Lord Judge, Mr Justice Owen and Mr Justice Griffith Williams that the wrong legal tests had been applied.
He said that the message was sent on a timeline on the Twitter facility to Mr Chambers's followers and not as a randomly searched for communication, and the relevant section of the Act was never intended by Parliament to deal with messages to the ''world at large''.
The circumstances of the offence of a ''menacing character'' had a higher legal threshold than that of a ''threatening character''.
Not all threats were menaces, counsel said.
To constitute a menace, he added, the threat must be of such a nature so that the mind of an ''ordinary person of normal stability and courage'' might be influenced.
Also, the person sending the message must intend to threaten the person to whom the message was sent - in other words, it was a crime of specific intent.
Mr Chambers's right to freedom of speech under the European Convention was engaged, he told the court.
Turning from the law to technology, he said that the 2003 Act did not ''bite'' as the social media platform involved was ''a content service'' and therefore outside the definition of both public electronic communication service and public electronic network.
