In the judgement, the Lord Chief Justice Lord Judge said Parliament represented "the conscience of the nation" when it came to addressing life and death issues, such as abortions and the death penalty.
"Judges, however eminent, do not: our responsibility is to discover the relevant legal principles, and apply the law as we find it," he said.
At the same hearing a third paralysed man won his case seeking clearer prosecution guidance from the director of public prosecutions (DPP) for health workers who help others die.
The man, known only as Martin, wants it to be lawful for a doctor or nurse to help him travel abroad to die with the help of a suicide organisation in Switzerland. His wife and other family want no involvement in his suicide.
The Supreme Court will also deal with the DPP's appeal against the Court of Appeal's ruling in Martin's favour.