The prime minister has promised he will comply the so-called "Benn Act" passed against his wishes by MPs last month, which forces him to seek a Brexit delay if he does not pass a deal through parliament.
But he has also said Brexit will definitely happen on 31 October - not explaining how this is possible given the legislation.
So campaigners - led by businessman Vince Dale, SNP MP Joanna Cherry QC and Jolyon Maugham QC - launched legal action at the Outer House of the Court of Session.
That was dismissed by Judge Lord Pentland on Monday, because of the "unequivocal assurances" Mr Johnson and his government gave the court they would comply with the law by trying to delay Brexit to avoid no-deal.
So the petitioners launched an appeal.
Aidan O'Neill QC, representing them, admitted arguing the court should write the letter asking for a delay if Mr Johnson refuses to was an "an unprecedented step, but these are unprecedented times".
The government's lawyer, Andrew Webster QC, claimed any interference from the courts could hamper the UK's negotiations with Brussels.
On Wednesday, three judges said they would not rule on the case until after 19 October - the point where Mr Johnson is forced to seek a Brexit extension to avoid no-deal.
James Matthews, Sky News' Scotland Correspondent, said the move amounted to "let's not get ahead of ourselves, effectively".