What role did religion play in the constitutional monarchies of Europe?

In some monarchies, especially in the old ones, they endowed the monarch (and also his dynasty) with a divine character, for example, the pharaohs of Egypt or the Roman emperors. Far from this conception of the king as a god, even in the 18th, although the States are non-denominational, some parliamentary monarchies are still linked to a certain religion. For example, Spain and Belgium to Catholicism, the United Kingdom and the Netherlands to Protestantism. There are many other examples, current and historical, such as that of the tsars, which, until before the Russian Revolution that ended the Romanov dynasty, were linked to the Orthodox Church.