If the verdict goes against Johnson, it could see parliament rapidly reassemble and would inevitably trigger questions about his position, having unlawfully advised Queen Elizabeth II to suspend parliament.
It would be the latest hammer blow to his plans for taking Britain out of the European Union on October 31, and pile huge pressure on his minority government.
It would also raise questions about whether he could hold out as premier long enough to face a general election, which recent polls suggest he could win with a large majority.
His setbacks in parliament and the courts have so far only increased his polling numbers, burnishing his reputation among those who voted to leave the EU, but his popularity could dwindle if he is blamed for dragging the Queen into the fray.
Whatever the decision, it is likely to provoke frenzied reaction, stoking up tensions in an already divided country.
- 'Father of lies' -
Johnson, who took office on July 24, insists suspending parliament was a routine and long-overdue move to launch a fresh legislative programme.
He also told Sky News on Monday that MPs will still have "ample opportunity to debate Brexit".
His opponents claim he did so to silence opposition to his plans to take Britain out of the EU, with or without a divorce deal with Brussels.
A ruling against the government would also throw a grenade into the country's opaque constitutional framework, representing a forray by the judiciary into the political arena.
Johnson was called the "father of lies" and accused of destroying parliamentary democracy during last week's three-day hearing, which heard two conflicting appeals against lower court decisions on the prorogation move.
Scotland's highest civil court found the suspension was unlawful, but the High Court in England said it was not a matter for judges.
The Supreme Court must therefore decide whether it even has the power to rule on such a case, before coming to any decision on the legality of the move.
David Pannick, representing campaigners appealing against the High Court ruling, argued that judges had the right to decide the proper scope of the prime minister's power to advise the head of state on shuttering parliament.
"This five-week prorogation has prevented parliament from carrying out its scrutiny functions over the executive over a period of exceptional length... for no rational reason," he said.
But Advocate General Richard Keen, the British government's top Scottish legal advisor, said it would see the courts straying into an "ill-defined minefield".
"This is forbidden territory. It is a matter between the executive and parliament."
- Biggest constitutional case 'of century' -
The 11 judges each express their own view, and have broadly five options.
They could decide it is not a matter for the courts, or decide it is within their scope but that Johnson acted lawfully.
They could rule that he acted unlawfully, but that the period of prorogation was not in itself unreasonable, meaning Johnson could decide to prorogue again in a lawful manner.
If they find he acted unlawfully and that he suspended parliament for an unreasonably long time, he will be obliged to recall parliament.
The court could also decide that because the prorogation was not lawful, it never really happened, meaning parliament remains in session.
"It would be ruling on the basis of general principle, and the general principle is that the government is accountable to parliament," professor Robert Hazell, from University College London's Constitution Unit, told AFP.
But even more consequential than the actual prorogation ruling will be the court's decision on whether political disputes such as this fall within its scope, he added.
If the judges decide they do, it would represent a "big step" in Britain moving away from a "political constitution" towards a "more tightly-regulated legal constitution."
"This is going to be the biggest constitutional case, certainly of the decade, and possibly of the century," he said.
AFP/File / KARL MALAKUNAS 
AFP/File / KARL MALAKUNAS 
AFP/File / Noel CELIS 
AFP / Philippe LOPEZ 
YOMIURI SHIMBUN FILES/AFP / YOMIURI SHIMBUN 
AFP / SAUL LOEB 
UKRAINIAN PRESIDENTIAL PRESS SERVICE/AFP / Handout 
AFP / SAUL LOEB 
Queensland Bats/AFP / Handout 
AFP/File / JACQUES DEMARTHON