The Supreme Court was today analysing claims brought by Leslie Moohan and Andrew Gillon at a hearing in London.
A courts spokeswoman said justices were considering a series of legal questions, including whether provisions prohibiting prisoner voting were incompatible with the European Convention on Human Rights and whether they breached the common law right to vote.
The prisoners' claims have already been dismissed by judges in Scotland.
Seven Supreme Court justices - including court president Lord Neuberger and deputy president Lady Hale - are considering provisions contained in the Scottish Independence Referendum (Franchise) Act 2013.
They were told that both prisoners want to vote in the referendum on September 18 but are not eligible under the Franchise Act.
The inmates say that prohibition is incompatible with their rights.
Their claims have been dismissed in Scotland by the Outer House and Inner House.
Lawyers for the two men are expected to complete their submissions later today.