The High Court has reserved its judgment in the landmark case taken by a lesbian couple seeking to have their marriage recognised by the State.

Ms Justice Elizabeth Dunne gave no indication when she would give her decision.

Dr Katherine Zappone and Dr Ann Louise Gilligan have taken their action against the State and the Revenue Commissioners.

They want the State to recognise their Canadian marriage or give them the right to marry here.

They say their constitutional right to marry has been breached, but the State denies any such breach.

In his closing submission, Senior Counsel for the women, Gerard Hogan, argued that the State's grounds for not allowing them the right to marry was based on the utterly wrong historical misunderstanding of homosexuality.