Paul Chambers, 27, said he thought that no-one would ever have taken seriously his joking threat to blow an airport "sky high".
Accountant Chambers 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.
But he was convicted at Doncaster Magistrates' Court of sending "a message of a menacing character", contrary to provisions of the 2003 Communications Act, fined £385 and ordered to pay £600 costs.
Today he asked two High Court judges to overturn a Doncaster Crown Court decision in November 2010 upholding his conviction and sentence - a decision which pushed the costs order against him up to £2,600.
Among his many supporters are fellow "twitter comedians" Charlie Brooker and Stephen Fry.'
The message he tweeted 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!"
Crown Court Judge Jacqueline Davies, sitting with two magistrates, said the electronic communication was "clearly menacing" and that airport staff were sufficiently concerned to report it.
She added: "We find it impossible to accept that anyone living in this country, in the current climate of terrorist threats, would not be aware of the consequences of their actions in making such a statement."
Today at London's High Court, Ben Emmerson QC, appearing for Chambers, argued the Crown Court had erred in law - and in common sense.
Mr Emmerson suggested it was hardly likely that anyone planning to blow up an airport would post their intentions on Twitter.
He told Lord Justice Gross and Mr Justice Irwin that conviction and sentence were normally meant to have a deterrent effect, but in the Chambers' case they had the opposite effect.
His conviction caused resentment and triggered an "I am Spartacus!" campaign in which 4,000 people tweeted the Chambers message across Twitter - "none of whom were arrested", said Mr Emmerson.
He added: "One has to inject common sense to avoid the law ending up looking silly."
He told the judges the questions for them were "whether this prosecution-conviction-sentence was a steam roller to crack a very small nut and whether it was a disproportionate response".
Today's hearing started with a joke and laughter. The judges had been asked before the start of the hearing whether members of the public could tweet the hearing.
Just before the judges entered Court 74, the court usher appeared at the front of the court and - waggling her fingers over an imaginary keyboard - announced: "You can twitter, as long as you behave!"
Mr Emmerson argued that the tweet was not menacing but just a joke. Chambers also lacked the necessary "mens rea", or intent, to be "menacing".
He added that Chambers' prosecution and conviction could not be justified. They were disproportionate and breached his right to freedom of expression under Article 10 of the European Convention on Human Rights.
Robert Smith QC, for the Crown Prosecution Service (CPS), disagreed.
He said the tweet was not viewed as a joke by those responsible for airport security.
It was posted at a time when the potential terrorist threat to airport security was high.
The law allowed for the restriction of freedom of speech when necessary in a democratic society.
Mr Smith said: "The prosecution and conviction (of Chambers) was a proportionate and necessary response to the nature of the message."
The Crown Court decision to uphold Chambers' conviction was justified by the facts of the case, said Mr Smith.
The judges reserved their judgment and said it would be handed down at a future date.
Among those sitting at the back of the court supporting Chambers were Pub Landlord comic Al Murray and Father Ted writer Graham Lineham.
Mr Murray, who recently hosted a special benefit performance for Chambers, said outside court: "I defend everyone's right to tell rotten jokes.
"This situation is Monty Python. It is absurd, bonkers. It means we cannot post what we want on Twitter, or say what we want - that is incredible to me."
Mr Lineham said the case had created confusion about the law.
He said: "There are thousands of messages every day that could be mistaken for threats."
He said of Chambers' tweet: "The problem is not that it was a joke, but it was a bad joke.
"My first series was full of bad jokes. If we were all to be convicted for bad jokes, we would all be in trouble.
"There is a disconnect between what is happening (in the courts) and what is happening outside, and they need to catch up or they will end up looking very silly."
A goodwill message was sent to Chambers by comedian Steve Coogan, who was featuring in another case at the High Court, in which his lawyers announced that his claim for damages for phone hacking had been settled at £40,000.
Among those sitting at the back of the court supporting Chambers were Pub Landlord comic Al Murray and Father Ted writer Graham Linehan.
Mr Murray, who recently hosted a special benefit performance for Chambers, said outside court: "I defend everyone's right to tell rotten jokes.
"This situation is Monty Python. It is absurd, bonkers. It means we cannot post what we want on Twitter, or say what we want - that is incredible to me."
Mr Linehan said the case had created confusion about the law.
He said: "There are thousands of messages every day that could be mistaken for threats."
He said of Chambers' tweet: "The problem is not that it was a joke, but it was a bad joke.
"My first series was full of bad jokes. If we were all to be convicted for bad jokes, we would all be in trouble.
"There is a disconnect between what is happening (in the courts) and what is happening outside, and they need to catch up or they will end up looking very silly."
A goodwill message was sent to Chambers by comedian Steve Coogan, who was featuring in another case at the High Court, in which his lawyers announced that his claim for damages for phone hacking had been settled at £40,000.
PA
