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The pair's appearance on the show comes after 'Idol' judges Katy Perry and Lionel Richie performed at the coronation concert Sunday.
The king and queen took their seats for their first event since Saturday's coronation.
Prince Louis pouts as the royal family waves to the crowd on the balcony of Buckingham Palace after King Charles' coronation service.
King Charles and Queen Camilla greet the crowd after assuming new titles at the coronation ceremony.
King Charles and Queen Camilla receive the royal salute after assuming new titles at the coronation ceremony.
The coronation featured several nods to the late royals.
The estranged prince attended his father's coronation, but stayed in the background during much of the ceremony.
Princess Charlotte waves to the crowd, following King Charles' coronation.
Queen Camilla gets crowned during the coronation service on Saturday at Westminster Abbey.
The 75-year-old wife of King Charles III received a historic new title on Saturday.
King Charles and Queen Camilla head from Buckingham Palace to Westminster Abbey via carriage ride ahead of his coronation.
The two were married from 1973 to 1995.
The royal couple traveled from Buckingham Palace to Westminster Abbey in the Diamond Jubilee Coach.
Check out the family members who attended the coronation.