In 1946, while still a student of Édouard Dethier at the Juilliard Graduate School of Music, Ajemian won the Walter W. Naumburg Foundation Award.

Among the many honors that have followed, the Order of St. James appointed her a Knight of Malta for her lifelong support of contemporary classical music.

With her pianist sister Maro Ajemian, she performed in Europe, Canada and throughout the United States in a wide repertoire including works which were written for them by such distinguished composers as John Cage, Henry Cowell, Alan Hovhaness, Ernst Krenek, Lou Harrison, Wallingford Riegger, Carlos Surinach, and Ben Weber.

[3] In the mid-sixties, Ajemian and her fellow violinist Matthew Raimondi founded the Composers String Quartet[1] at the suggestion of Gunther Schuller, which quickly earned an international reputation and toured in more than 26 countries, including the Soviet Union, India, the Middle East, Africa, Australia, Japan, Southeast Asia and China.

For many years, they were the primary performers at the Mt Desert Festival of Chamber Music in Northeast Harbor, Maine.