Catherine of Aragon (1485-1536), married to Arthur Tudor and famously to Henry VIII of England, was an early candidate for marriage - political, as were most marriages between royal houses - into England. Her mother, Isabella I, had an arguably stronger claim to the throne of England than Henry VII due to his legitimized (originally born out of wedlock) ancestral connection to John of Gaunt. Additionally, and unusually, both of Catherine's parents were reigning sovereigns in their own right, part of one of the most powerful dynasties in Europe. Catherine represented a large dowry and secured legitimacy for a dynasty, and a strategic alliance. Arthur was close in age with Catherine, which was a marginal bonus. They were wed by proxy in 1499, but they only met when Catherine landed in England in 1501 when she was fifteen years old. They married, for a second time, ten days after their first meeting, a formality but also of cultural importance. Around this time, payment of the first half of the 200,000 ducat dowry was completed.

Catherine and Arthur corresponded prior to their meeting, and Catherine traveled with her own retinue including a diplomatic representative (a nobleman) to stand in for her father. Diplomacy to arrange the marriage was carried out by correspondence and diplomats, court functionaries. I'm not aware of the behind the scenes conversations in Iberia and England, or the extent to which Catherine or Arthur had a say in to whom they were married. In England less than half a century earlier, Edward IV famously chose his own bride in Elizabeth Woodville, yet he was a reigning monarch.

big party and dinner where he'd invite leaders from other kingdoms and she could meet her suitors there and after him and the Empress would decide who was best for her based on the political advantages and how the his and the leaders he'd be meeting with's visions for the future seemed to align based on the meeting.

It was considered, in some countries, gauche to attempt to arrange a cattle call interview for a spouse, especially if those invited were of more powerful or storied dynasties. With the genders reversed, this would be unlikely unless your protagonist is the leading heir. This is an era of strict, although with variations by circumstance or culture, enforcement of gender norms and men were usually the preferred heirs (some nations, such as France - Salic Law, prohibited women from inheriting titles or property). It would be even less likely for reigning monarchs to attend a foreign meeting with their heir. For example, an heir was a frequent hostage for their parents release if captured in battle amongst nobles.

I'm going to go with 15th/16th century England, since you said you're not picky about time period.

You're not going to invite a bunch of possible husbands to a big dinner in order to pick the best one. For one thing, you don't need to meet them. You don't really care if a guy is good-looking or has a great personality, or anything else that you could only find out by meeting him in person. This is a political deal, remember, not a personal matter. You already know which other royal and noble families have heirs available for marriage. You know where you need to strengthen alliances, and where you don't need to bother because the ties are already strong enough. And you know what assets the princess and each possible husband will bring to any marriage, both in terms of land and titles, and in terms of family connections and political clout. Based on these criteria, you can come up with a pretty clear wish list, in order of priority. You don't need a political bachelorette contest. You only need to work with your top choice, not with all of them at once.

For another thing, that party would be a horrible idea, politically. You invite a bunch of rulers to make a long journey from all over Europe, after which you tell most of them 'Nah, we can do better than you, bye'? They're going to be pissed. Unless you're much more powerful than they are, you just insulted a whole bunch of powers whom you would really rather not insult.

Also, you're unlikely to wait till the princess is ready to get married before you get her betrothed. She's a highly useful strategic commodity, and her father and his advisors (who may or may not include the queen, depending on various factors) want to make sure they use her to full advantage. By the time she's a couple of years old, you're keeping an eye out for the most advantageous alliance. And you want to get that alliance in place as soon as possible. You're not going to wait around till the princess is old enough to actually get married. You're going to get her good and betrothed long before then.

Let's look at Katherine of Aragon, for example. She was born in 1485, the youngest daughter of King Ferdinand of Aragon and Queen Isabella of Castile. Henry VII picked her out very early as a possible wife for his eldest son and heir, Arthur. Henry was a little shaky on the English throne, which he'd taken by conquest from Richard III, and he wanted to solidify his heirs' position. While he did descend from John of Gaunt, it was via an illegitimate line, so not all European kingdoms accepted Henry's blood right to the throne. Katherine, on the other hand, was descended from John of Gaunt by legitimate lines; by getting her into the family, Henry VII could silence any doubts about his family's right to the throne. There was also the fact that Spain was newly united and on its way to becoming a hugely important political force within Europe. So Katherine came with a lot of political capital.

And Henry wanted to secure that capital fast, not wait around till she and Arthur were of marriageable age - by which time someone else would probably have nabbed Katherine. Katherine and Arthur were betrothed when she was three. They didn't meet till they were fifteen and had already been married by proxy.

Or let's take it a generation forward and look at Mary Tudor, Katherine's daughter by Henry VIII (Arthur's brother, whom she married after Arthur died). Henry spent much of Mary's childhood negotiating possible marriages for her. When she was two he betrothed her to Francis, the Dauphin of France. A few years later that contract was dissolved, and when Mary was six, Henry betrothed her to the Holy Roman Emperor Charles V. Charles broke that one off, and Henry went back to the French, eventually negotiating a treaty that said Mary would marry either the King himself or his second son. That one got ditched as well, though, when Henry's advisors worked out an alliance with France independent of any marriage - meaning that Mary was an asset who could more usefully be deployed elsewhere.

Or let's take it a generation back and look at Henry VII's wife, Elizabeth of York, daughter of Edward IV. She was born in 1466. When she was three she was betrothed to George Neville, but his father joined in a rebellion against her father, so that was the end of that. When she was nine she was betrothed to the Dauphin of France, but his father called that off. When Edward died and Elizabeth's uncle Richard became king, he started negotiating to marry her into the Portuguese royal family. Finally her mother formed an alliance with Henry's mother, and she was betrothed to Henry - because he was gunning for the throne, but again, his blood claim was weak. Being married to Edward IV's daughter helped to bolster it.

Basically, if you're only arranging a betrothal for your princess when she's actually ready to get married, it almost definitely means that at least one betrothal has fallen through along the way.

So once you've decided who's at the top of your wish list, how do you arrange the marriage? Probably the king sends over a trusted advisor - the way Henry VIII sent Cardinal Wolsey to negotiate Mary's French marriage, or Thomas Cromwell to negotiate his own marriage to Anne of Cleves - and the various advisors come to an agreement and hammer out the details of the marriage treaty. Once the princess and her fiancé are old enough, you probably have big-name painters paint portraits of them to exchange - although those portraits might well be on the flattering side, and they might get a Tinder-style surprise when they meet in person, like Henry being disappointed in Anne of Cleves's looks and feeling that he'd been misled by her portrait. They might correspond: Katherine of Aragon and Arthur wrote to each other for years before they met - in Latin, which was the only language they had in common. (When they actually met, they discovered they could barely talk to each other because their Latin pronunciations were so different.) But they might well not meet till soon before the wedding.

If the princess is the heir to your throne, then things are complicated by the concept of jure uxoris. This means that if she marries, her husband will legally take over both her lands and her title. He won't just be the king consort; he'll be her co-ruler. So you need to be very, very careful in choosing him, because you're essentially handing over your country to him. And you're going to want to make sure that the marriage treaty is very, very carefully negotiated. You may need to actually enact legislation to manage this situation. This was an issue for Mary Tudor, when she became England's first queen regnant after her father's and brother's deaths: any marriage she entered into would have ferociously complicated political and religious implications for England. When she decided to marry Philip of Spain, Parliament passed a specific Act establishing the terms of the marriage, in order to ensure that England wouldn't become essentially just a Spanish territory. The Act stated that Philip would be given the title of King of England, but only for Mary's lifetime - if he outlived her, he wouldn't continue to reign. It stated that Parliament would be called in both their names. The Act also prohibited Philip from appointing any foreigners to office in England, or from taking Mary or their potential children abroad, and it stated that England wasn't obliged to provide military support to Philip.

As you can see, maintaining your country's sovereignty when you're marrying off a queen regnant (or, in your case, someone who's apparently going to become a queen regnant) is complicated stuff.