Examples
"God Save the Queen" is the royal anthem in the United Kingdom, Canada, Australia and the other Commonwealth Realms. In the United Kingdom it also serves as the national anthem. In New Zealand, both "God Save the Queen" and "God Defend New Zealand" are official national anthems, although "God Save the Queen" is only used when the Queen or a member of the Royal Family is present.
"Kungssången", literally The King's Song, is the Swedish royal anthem.
"Kong Kristian", King Kristian, is the Danish royal anthem.
"Marcha Real", literally Royal March, is the national anthem of Spain
"Phleng Sansoen Phra Barami", the royal anthem of Thailand
"Kongesangen", literally The King's Song is Norway's royal anthem. It is actually a Norwegian translation of "God Save the Queen" and uses the same music.
"Боже, Царя храни", God Save the Tsar, literally God, Keep the Tsar, was the national anthem of the Russian Empire until 1917. It is still used in some circles of the Russian diaspora.