This is a tough question to tackle because of its broadness, but from my own research, I find evidence of medieval kings believing in the divine appointment of other monarchs when the source of that divine appointment was the Papacy. Here’s an example:

Roger II fought for much of his reign to receive recognition from the Papacy that his kingdom, the Kingdom of Sicily, was legitimate and that he thus ought to be honored with a Papal coronation. Since the Pope was the representative of God on Earth, this was divine recognition. Roger II was first crowned by an anti-Pope in 1130 and then by the real Pope in 1139. Some kings in Europe, like Conrad III of the Holy Roman Empire, fought to keep Roger II from being recognized as king because then Conrad’s claim to the lands of Sicily and southern Italy would be much less strong. When the Pope crowned Roger II in 1139, Conrad was effectively forced to recognize the legitimacy of the Kingdom of Sicily and the appointment of Roger.

Once Roger II received a legitimate papal coronation, he flaunted it in his royal imagery. This is most clearly seen in a mosaic from the mid-1140s in the Martorana, located in Roger’s capital of Palermo. Here God is bestowing on Roger a crown to signify his rule as a legitimate monarch over the legitimate Kingdom of Sicily (interesting sidenote: Roger is departing from Latin Christian tradition here, in which kings are usually given their crown by the Pope, and he is instead following Byzantine precedent by having God crown him — this is a not-so-subtle jab at the Papacy, which had caused Roger a lot of trouble during the early years of his reign).

I hope that is an appropriate answer for your question. I’m sure there are numerous other examples from the Middle Ages to show the importance of Papal recognition to legitimate kingship. I can remember off the top of my head a Papal Bull of the mid-14th century that permitted the Scottish kings the right to be crowned. There are bound to be other great stories about the fascinating intersection of papal and imperial authority.

Abulafia, David. “The Crown and the Economy under Roger II and His Successors.” Dumbarton Oaks Papers 37 (1983): 1–14.

Britt, Karen. “Roger II of Sicily: Rex, Basileus, and Khalif? Identity, Politics, and Propaganda in the Cappella Palatina.” Mediterranean Studies 16 (2007): 21–45.

Houben, Hubert. Roger II of Sicily: A Ruler between East and West. Translated by Graham Loud and Diane Milburn. New York: Cambridge University Press, 2002.

Loud, Graham. Roger II and the Creation of the Kingdom of Sicily. New York: Manchester University Press, 2012.