It seems like kings and noblemen were ordering lots of fantastically decorated harnesses in the 16th century. When an order was made (I'm guessing to a prolific armourer), what input would the client have? I'm guessing he would've outlined the type of armour he's ordering (field armour, tournament armour, half-armour etc.) Could he demand certain colours, designs, and so on? Could he ask for different types of helmets or cuirasses?
Part 1
This is a great question. You are absolutely right that there were a lot of great, grand harnesses put together in the 16th century. First off, I answered a similar, broader question about the 15th century here.
But since we’re talking about royalty, and the 16th century, there are even more types of customization that are available. The short answer is that as a 16th century monarch you could have whatever your royal heart desired (though practicality and fashion generally kept armours restricted to contemporary forms...unless you talked to Fillipo Negroli) Moreover, you would have control over every aspect of the process, because you are the king, and it’s good to be the king. Because your royal power is so broad, I’m going to expand this question to include every step of the armouring and ordering process. I’m going to focus on the first half of the 16th century since that is where the most is going on with armouring as an art.
So let's get started, your majesty.
Your first choice will be what armourer you employ. This is important because while a good armourer will give you a lot of choices (see below), their own training, traditions and strengths will influence the form of an armour.
You may already have a court armoury, like the one that Emperor/Duke Maximilian established in Innsbruck in the first decade of the 16th century. As kings gain more power and centralize their authority, the position of ‘court armourer’ is changing. Before, court armourers were simply armourers with their own shops who had a sinecure or warrant to act as official armourer of the court, the Groszschedels of Landshut in Bavaria, or like the position the Missaglia had with the Dukes of Milan in the last century. But increasingly your fellow monarchs are -building- armouries and taking on armourers on retainer as employees of the court. If you’re building an armoury, you’ll need armourers, and you’ll have your pick, since you have the guilders/florins/marks/thaler. If you feel the need to build a royal or Arch-ducal armoury then you may not be happy with the local armourers for some reason (not good enough, not fashionable enough, not fancy enough), so perhaps you want a foreigner. What about an Augsburger? Maximilian got one (Seusenhofer) to move across the Bavarian Alps to Innsbruck, and if the Habsburgs like it, it has to be fashionable. But if you’re a king in the North of Europe, what about a Fleming? Or an expatriate Lombard like all those Milanese armourers who seem to find their way -everywhere- from Spain to London to Burgundy? Then you need to buy the supplies - anvils, stakes, horned bikiron for shaping things, tongs, and more hammers than you have ever seen in on a receipt in your life. Don’t forget the water wheel for polishing, and the mill race to go with it and everything besides. But it is worth the expense, because you are worth the expense, your majesty.
So now things are up and running and you’re ready to order. Suppose, though, you’ve picked your armourer, and you’re not happy. Maybe he goes back to Landshut because he dislikes the climate, maybe he’s not good enough, or maybe you can’t help but notice that the Emperor’s ambassador at the Shrove Tuesday tournament had more fashionably shaped and splendidly etched and gilt armour than you. That armet’s chin looked just right, and the pauldrons had haute pieces that rose at just the right angle, and the neckline of the breastplate reminded you of your favorite doublet. And that etching! Was it Hopfer - it looked like Hopfer. Maybe you spend your Ash Wednesday fast trying to figure out who made his harness, and what you would need to do to get him to work for you. It isn’t exactly a pious fast, but you’ll be damned (heh) if you’re going to let the Emperor’s ambassador show you up in your own country.
This is all very much like the process Henry VIII went through in creating his armoury at Greenwich. First off, we don’t know why he did so. Alan Williams has implied that heat treating armour was a trade secret unknown in England and that English armourers weren’t technically skilled enough in general, but Tobias Capwell suggests that it may have simply been fashion. Capwell recounts the impression that Philip I’s armour made at court in the early part of Henry’s reign. Then, around the time that he was establishing his armoury, Henry received a visit from Emperor Maximilian, who presented him with an extravagant gift armour, which maybe have included a helmet for the field and definitely include a helmet with a fanstical parade visor and horns. Capwell argues that it was the fashion and splendor of the continental armour of the Habsburgs that impressed Henry, not its superior metallurgy. Regardless, it is clear that Henry didn’t like the armour he had available domestically for some reason, so he created a whole new armoury. As he was establishing the armoury, Henry turned to different sets of armourers - Flemings, Italians, and more Flemings, mixed with ‘High’ Germans, the ‘Almains’. All of these offered some more ‘continental’ flavor - the Italians were associated with both the greatest armouring center in Europe and with the seat of renaissance culture, while armourers from both the Low Countries and the Southern German lands were known to serve the House of Habsburg. It was these Almains who would run the armoury for the next half century and in time transform it into the one of the most technically proficient armouries in Europe.
.So, you may desire a certain armour so much that you build an armoury to make it for you. Or you may decide to engage a great armourer that is still independent - you are the king of Denmark or Sweden or Scotland and do not yet have an armoury of your own, or perhaps you are like the Habsburgs, and having a court armoury doesn’t prevent you from ordering elsewhere. Indeed, is the house of Habsburg not famous for ordering their harnesses from the Helmschmieds of Augsburg? The young Charles is the fourth generation of Habsburg to be armoured by a Helmschmied. Different armourers have their strengths - the Helmschmieds make fine war harnesses that are pleasing to the eye, while, (beginning in the 1530’s) the Negroli brothers make parade armours the like of which the world has never seen. So your choice of an armourer will be affected by the sort of armour you want, and the armourer you choose will affect its final form.