The Court of Appeal has dismissed two separate applications for permission to bring petitions challenging the yes result of the same-sex marriage referendum.

The decision means the referendum returning officer can now issue the certificate confirming the result of the 22 May poll.

A stay on the issuing of that certificate had applied pending the appeal court's ruling and has now been lifted.

The three-judge court rejected arguments by Gerry Walshe, an electrician, of Lisdeen, Co Clare, who had established the necessary grounds to bring a petition.

The court also found Maurice J Lyons, a gardener, of Callan, Co Kilkenny, had made out no basis entitling him to bring a petition.

Both men argued they should not have costs awarded against them, because they brought their applications in the public interest and because they believed the views of those opposed to same-sex marriage were not represented by the State during the referendum campaign. The court awarded costs against both men.

In a decision that concluded after 6pm Mr Justice Sean Ryan, Ms Justice Mary Finlay Geoghegan and Mr Justice Michael Peart ruled there was no basis on which the court could grant leave for a petition to be brought by either man. A number of supporters of the yes and no campaigns were in court.

Mr Walshe had provided no evidence to support his claims the outcome was affected by an unlawful spend of public monies, Mr Justice Ryan said.

Mr Walshe had claimed millions of euro was provided to various organisations, including charities, but had provided no proof any such monies were public monies, he said.

Mr Walshe had also not established any wrongdoing or irregularity, as required under the Referendum Act, for a petition to be brought.

His claims that the Garda Representative Association was not entitled to advocate a yes vote, or that the Taoiseach had refused to participate in debates with no campaigners, were not grounds on which a petition could be brought, he said.

Claims that the referendum process was invalidated by identifying marks on ballot papers, which damaged the secrecy of the ballot, were based on a "completely mistaken" view of the relevant law that provides each paper should have a mark, he said.

Other complaints about An Post issuing a St Valetine's Day love stamp with an equality symbol, which Mr Walshe alleged amounted to a "subliminal message" in favour of a yes vote, were also dismissed.

Mr Justice Ryan said the threshold for a petition is a high one and Mr Walshe had to show any complaint he advanced would have materially affected the result. He had failed "and failed significantly", to do so on each and every point he had raised.

Dealing with Mr Lyons' appeal, the judge said arguments the Constitution could only be amended by a proposal initiated by the people themselves were based on a "fundamental misunderstanding" of what the Constitution says, what it means and what the powers of the courts are.

Mr Lyons also erred in arguing the sovereign people cannot approve amendments that contradict other provisions of the Constitution as any amendments approved were a matter for the people, the judge said.

The judge added the courts cannot say to the people they cannot vote in favour of a particular measure as that was precisely the people's own function.

The judge rejected further arguments that those members of the electorate who do not vote in referendums must be regarded as no voters. Mr Lyons' arguments in that regard were "contrary to principle" and "contrary to common sense".

In this referendum, there was a substantial majority in favour of the proposal but that was irrelevant as the Constitution provides a proposal is approved if passed by "a majority" in a referendum, the judge said.

Mr Lyons' arguments all come down to a rejection of the majoritarian principle and that "simply does not arise".