The Principality of Liechtenstein is sandwiched between Austria and Switzerland. It is a hereditary principality with political powers shared equally between the elected parliament and the prince. Nobody knows what happens if ever they should agree to disagree because there is no proviso for a resolution process. The prince is also head of state.
Among the dwarf states of Europe, the Principality of Andorra is the largest. Until quite recently, it was an absolute monarchy. It was governed not by one, but two princes, and both are not citizens of Andorra. They don't even live in Andorra. To make the case even more curious, it is not a hereditary monarchy.