The case could have implications for dozens of former prisoners in England, Wales and Northern Ireland.
Judges will clarify the position for three men refused compensation after their murder convictions were quashed.
Lawyers for Barry George - cleared at a retrial of killing BBC presenter Jill Dando - also took part in the hearing.
Mr George spent eight years in jail before being acquitted in August 2008 of Ms Dando's murder.
The High Court later ruled he was entitled to a judicial review hearing over the government decision to refuse him compensation of up to ￡500,000.
Beyond reasonable doubtPeople who have been wrongfully convicted are entitled to compensation only if they can show there's been a "miscarriage of justice".
But the meaning of the phrase has been unclear since a Law Lords ruling in 2004 which came up with different definitions.
The version adopted by the government has resulted in compensation being denied to people because they could not prove their innocence beyond reasonable doubt.
The men involved in the Supreme Court case have seen their claims for compensation rejected despite them being cleared by the Court of Appeal.
The main case in the proceedings involves Andrew Adams, who spent 14 years in jail after being wrongly convicted of murder.
Mr Adams, from Newcastle, was found guilty in 1993 of shooting retired science teacher Jack Royal, but released in 2007 by the Court of Appeal.
The High Court later rejected his compensation bid, and Mr Adams took his case to the Court of Appeal.
The two other cases are from Northern Ireland.
BBC home affairs correspondent Danny Shaw says if the court widens the meaning of "miscarriage of justice" the government will have to reconsider Mr George's claim - along with many others that have been turned down.
However, the judgement is unlikely to affect Scotland where there are fewer restrictions on eligibility for compensation.
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