The brothers' music has attracted worldwide attention and brought them to audiences from Togo in West Africa to Carnegie Hall in New York City.
Seathrún, who gave up his desire to work as a professional harpsichordist, plays piano, guitar, a number of different flutes, and bouzouki.
The brothers repeated the state honour about a decade later during then-U.S. President Bill Clinton's peace-promoting trip to their country.
The group has toured throughout the United States, including stops in New York at St. Patrick's Cathedral and Radio City Music Hall.
They have performed classic Irish songs, such as "Bó na Leathadhairce", "Báidín Fheilimí", "Peigí Leitir Móir" and "Beidh Aonach Amárach".