From an this earlier answer:

In medieval Europe, so-called posthumous births counted towards inheritance of titles, including the throne...when people wanted them to count. That is to say: when sexism, the psychological/proto-nationalist importance of the ruling dynasty, the desire of the high nobility for stability versus their own independence, and in one case, the sheer audacity of the queen and her lady-in-waiting aligned properly, succession indeed passed from the deceased king to the son he would never meet.

But even then, there were problems. I want to look at three cases of posthumous succession to demonstrate that whatever the law actually was, posthumous succession was a deeply vulnerable moment for the dynastic family.

The first case is West Francia in the ninth century, several generations descended from Charlemagne. During his lifetime, King Louis the Stammerer (r. 877-879) had two sons and two daughters by his first wife, and one daughter with his second wife. She was pregnant when he died, and ultimately gave birth to a son.

No problem, right? Two perfectly normal, legitimate, in-lifetime sons! In fact, Louis III and Carloman II ended up jointly inheriting (oh, Carolingians). The problem was, the two of them also died quickly, and right after each other (882 and 884).

Now, West Francia was nominally a monarchy, but in reality, its nobles exercised far more power than the king (Louis III spent basically his entire reign trying to quell one rebellion). With Louis II's in-lifetime sons both dead, the West Francia nobles saw their chance. They railed Emperor Charles the Fat into seizing the crown. Why? Because Charles had plenty of territory over his own, and rather preferred his huge tracts of land that did not lie in West Francia. They wanted an absentee ruler who would let the nobles be the nobles--and that's pretty much what they got. (Except for that one pesky time Charles promised to fight Vikings, and fought the nobility instead...oops.)

But the nobles of West Francia, it turned out, had conflicting agendas beyond simply "more power for us." When Charles the Fat died, one group thought that a king with military skill who had promised to fight Vikings and actually fought Vikings was a good idea, and designated Odo, then count of Paris, as king. But Odo's authority did not look so good from elsewhere in West Francia. And this particular group remembered that, somewhere in the mists of long ago, Louis II actually had had three sons. They hauled in Charles the Simple, or rather, Charles' advisor-mentor-power-holders, and plopped a crown on his head.

So this is a case of posthumous birth counting...when it was good to count.

One notable point of the West Francia imbroglio is that at no time were Louis II's daughters (at least two of whom were alive at the time of Carloman's death, and at least one upon Charles the Fat and Odo's deaths--we lack further information) considered to inherit the throne. But as the centuries wore on, women inherited and ruled counties and principalities, even kingdoms, in their own right. Conceivably, this could have been true in France as well: the Salic law that we all know from Shakespeare ("In terram Salicam mulieres ne succedant / No woman shall succeed in Salic land") wasn't codified until the later 14C, or even proposed formally until earlier in the same century.

And in the early fourteenth century, the sunset of the Capetian dynasty, posthumous births allow us to see support for that sort of inheritance principle in the making.

Philip the Fair (r. 1285-1314) was quite the powerful and authoritative king. He faced down a pope and brought the papacy itself into his own country; he orchestrated the destruction of the Knights Templar. And he left an ample number of sons--three, in fact--and one daughter. Isabella's marriage to the king of England would serve her well as queen and queen regent, but things did not work out quite so well for Philip's sons. At the very end of his reign, the king who had spent his life cultivating a reputation as the most pious, the spiritual successor to Louis IX, publicly accused and punished his sons' wives for adultery.

Philip proceeded to die almost on the spot, and his oldest son inherited the throne as Louis X--great, fine. Well, it won't do to have an adulterous queen of France, right? And so Louis had Margaret, with whom he had one daughter, murdered in prison. Louis promptly remarried and impregnated Clemence of Hungary--and died, perhaps of too vigorous a tennis match (or perhaps poison).

And this is where things get confusing.

Louis X's next-in-line brother Philip future-V seized power. Was he regent or uncrowned king? Clemence gave birth to a son, John, who only lived for six days. Was John the king of France? When a later John assumed the French throne, he would be called "the second," thus recognizing the six-day kingship of Louis X's posthumous son. But at the time, it's less clear. Ceremonial for kings had become tremendously important as not just a show but an exercise of power in the late Capetian years. Coronations of kings, of course, but also coronations of queens and--a prophecy of the coming focus on the art of dying well--funerals. The passage of power from one king to another was wrapped up in enormous Christian and political significance (and also, didn't the power to cure scrofula have to be transferred in person?).

And John, well...John didn't get any of this. Barely a blip, whereas Philip V had made sure not only were Louis' two funerals splendid, but Philip's role was Known. Was John ever "really" king?

One way or another, Louis' brother Philip forcefully argued that Jeanne, Louis' in-lifetime daughter with Margaret, could not inherit the throne out of legitimacy questions, and formally took the throne as Philip V.

Philip and his wife Jeanne had children, but they were daughters, and despite being cleared of her own adultery accusations, there may have been lingering questions. And Louis and Philip's younger brother, Charles the future IV, hungered for his chance. When Philip V died also rather quickly, Charles jumped the line of succession in place of Philip's daughters. This assertion of male right to inherit even when it interrupted an existing direct succession, though it gave Charles the throne he wanted, would pretty much end the mainline Capetian ruling dynasty.

Charles also died quickly--leaving one daughter and a pregnant wife (another Jeanne...welcome to the Middle Ages). The nobles were willing to wait out the pregnancy. As regent, they chose the next closest male to the throne, Charles of Valois' (the orchestrator of Philip V and Charles IV's reigns) son Philip.

But when Jeanne gave birth to another daughter, the Valois and supporters had precedent: even before the formal entrenchment of the Salic principle, women could indeed not succeed. The throne was Philip's.

The last years of the great Capetian dynasty, thus, show the ad hoc treatment of posthumous births in medieval Europe and the hardening of prejudice against women's rulership, and provide a preview of the years when succession would be governed by more formal laws. Of course, some of those laws would go on to be a bit of a problem: the English claim to the French throne, you know, that little war that lasted more than a century, rested on the principle that while women could not rule themselves, the throne could be inherited through them to the next closest male heir.

And THAT question, my friends, would prove pivotal in my last and best example of posthumous princedom in medieval Europe: that time the Queen of Hungary stole the crown.

No, literally.

It's Complicated how this happened, but suffice to say that in 1437, Elisabeth of Luxembourg/Hungary (also Complicated, thanks to a certain saint) sort of inherited the Hungarian throne from her father, but really the Hungarian nobles recognized her husband Albert instead. The previous generation had shown that the throne could be transferred through women, but not held individually by them--a crucial precedent.

Elisabeth and Albert had two daughters, and quite soon after their ascenion to power (1439), Elisabeth was pregnant yet again--and then Albert died.

With two daughters and the throne transferrable through women, by marriage (how Elisabeth's father had gained power), Elisabeth became a prime target for marriage by Polish nobility who wanted that Hungarian territory annexed to their own. But Elisabeth was not giving up. So, in possibly the best heist of medieval Europe (it involves trick entrances and setting a castle on fire), Elisabeth conspired with her lady-in-waiting/handmaid, Helene Kottaner, to steal the actual, physical crown of Hungary.

Now, as I've discussed elsewhere, crowns themselves multipled like castles in medieval Europe, a crown for every occasion. But this particular one was the ceremonial coronation crown, and its material presence was crucial to recognition of the king.

Elisabeth and Helene stole it for her son.

The Polish nobility and various Hungarian factions were not so easily stopped, and of course matters devolved into multiple kings and civil war and palace intrigue. Ladislaus the Posthumous is counted king of Hungary today, of course, but his reign was filled with regnal and regional regents (say that five times fast), the noble elite's very big problem with some of those regents, nascent Bohemian/Hussite proto-nationalism, and all sorts of the ugliness that results from an unclear succession.

So these three examples are, of course, examples. But they illustrate nicely the clashes between the ideological desire for a stable succession that comes with parent-child dynastic inheritance, strategic sexism, and individuals' desire to maximize their power.