Monarchy that is considered democratic because ultimate authority is held by elected officials

Depends. Firstly monarchy can refer to such situations as found in the Middle East where kings (monarchs) rule with complete power. Even though they have advisers in multiple country the monarch has the ultimate power. Constitutional monarchy, one where there is no power invested in the monarchy, is democratic and the queen/king and her association does not get involved in the political process and all power in held by a parliament (like in the UK). It can become even more loose like in my home country, Australia, where the queen is represented by the governor general. However the governor general (seen as the crown (the monarch establishment)) must sign off laws and has booted (removed) Gough Witlam (a prime minister) out of his office!