The term was introduced into English political and historical discourse by Edward Augustus Freeman, in his History of Federal Government (1863).
The head of state of the federation was a monarch, the German Emperor, who was also head of state of the largest constituent part to the federation as King of Prussia; other constituent monarchies, such as the kingdoms of Bavaria, Saxony and Württemberg and various grand duchies, duchies and principalities, retained their own monarchs and armies.
For example, modern Italy had not unified until Risorgimento of the late 19th century, with the several smaller kingdoms, duchies, republics, etc., each headed by a different dynasty or ruling class, being disestablished in favor of a unitary monarchy under the house of Savoy.
Currently, the term can be applied in the fullest sense to the United Arab Emirates and Malaysia.
While not officially declared as such, Spain has been referred to as a federal monarchy, due to having many autonomous communities helmed by presidents who all answer to the Spanish crown.