The President, Mrs McAleese, said she had been impressed by the transformation of society in Oman in the 30 years since her host, Sultan Qaboos, took over.
Her four-day state visit ends this morning, and last night she attended a private dinner with the Sultan at his main residence, the Al Baraka Palace. She arrives back in Dublin tonight.
The two heads of state had earlier exchanged gifts. The Sultan gave the President two solid silver trays with an embossed design, and she gave him an original Waterford crystal lamp with an engraving of the harp and a bronze of a horse and foal.
Before last night's dinner Mrs McAleese said the Sultan had created a future for Oman on its own terms. He obviously had great power and had learned from other places to maintain his country's culture and architecture while nudging it forward, particularly in the areas of education and women.
People told her, she said, that 30 years ago he was concerned about the environment. No one had known what he was talking about; now they were grateful. The highlights of her visit, Mrs McAleese said, had been her first discussion with Sultan Qaboos when he spoke about Muslim women and the future, and her meeting yesterday with the Omani Women's Association.
The members felt they were on the threshold of a new experience and had great hopes for themselves and their children, she said.
Yesterday had been a day of relaxation for the President after a heavy earlier schedule. Later she attended dinner accompanied by Dr Martin McAleese; the Minister for Social, Community and Family Affairs, Mr Ahern; the Minister of State for Enterprise, Trade and Employment, Mr Tom Kitt; and the Ambassador, Mr Conor Murphy.
Earlier yesterday the President toured the royal stables on the coast north-west of Muscat. In the humid heat of 30 she was shielded from the blazing sun by a canopy as several dozen Arabian thoroughbreds were led by their grooms round the parade ring.
The stables and stud face the beach. Public race meetings are held there eight or nine times a year on the 1,400-metre sand racetrack, which is a centrepiece of the magnificently manicured establishment.
From there, the visiting party went to the Omani Women's Association, where they were greeted by clapping and singing girl guides. Seated on cushions lined against the walls of a huge carpeted room, they were entertained by traditional barefoot singers and dancers.
They toured an exhibition of traditional women's dress, and some of the party, but not the President, had their hands decorated with henna.
Mrs McAleese's visit has received extensive coverage in the local papers, both Arabic and English. Irish flags decorate the main city highways, although they are not as numerous as the pictures of the Sultan, which adorn every second lamp-post to mark the 30th anniversary of the coup when he took over from his father.