Drop bear asked this question in the latest Bujinkan thread and I thought it deserved an answer. Since it's not directly relevant to discussion of the Bujinkan, I pulled it out for a separate post.
To begin with, HEMA (Historical European Martial Arts, for anyone who doesn't know) is not about re-enactment or play acting or passing on the societal values of a medieval knight or peasant or burgher, so that part of the question is irrelevant.
In general, HEMA is concerned with learning to fight using specific weapons and martial systems that were used by Europeans during an historical period ranging from the 14th century (the earliest treatise we have to work with comes from around 1300) to the 19th century. Most of these systems aren't directly applicable to modern application, since dueling with swords has inexplicably fallen out of fashion.
So why do we do it? Because it's fun. Some people like throwing balls through hoops, we like hitting our friends with swords.What separates HEMA from LARPing is a couple of concerns. First, we want our practice to reflect the way historical practitioners of these systems actually fought, rather than something we just dream up from our imagination. Second, we want to develop actual functional skill. So if we are studying a sword art then we would want to be able to effectively defend ourselves with a sword if we were attacked by an opponent who was also wielding a sword.
So, how do we get to that "accurate" practice? It's a multi-step, iterative process with a lot of problems to solve.
Problem: how do we know what these historical martial practices actually were? There are only a small handful of surviving "living" historical European martial lineages handed down from teacher to teacher. Those present a slightly different set of challenges, so we'll set those aside for the moment. The primary starting point for most modern HEMA practice are treatises written by fencing instructors who were teaching these arts at the time. For example, my club practices the art laid out in a fencing manual written in 1570 by Joachim Meyer, a professional fencer and master-of-arms for the Duke of Schwerin.
Problem: How do we know whether the writers of these treatises actually knew what they were talking about and weren't just peddling medieval bullshido? We have a few possibilities. We can look at the historical record to see what it known about the writer's life and reputation. Presumably it would have been harder to maintain one's status as a respected and influential fencing instructor while peddling bullshido in an era when people actually dueled and fought on the battlefield with real swords regularly than in the modern era. Some of the later sources were actual military manuals (infantry and cavalry saber, in particular). It seems likely these were based on actual battlefield experience. We can compare the information in a given treatise to what is taught in other contemporary treatises and what is depicted in contemporary artwork. Finally, we can test whether the methods taught seem to work effectively in sparring. (More on this later.)
Problem: Do we understand the context in which a given art would have been applied? A system developed for unarmored civilians dueling to first blood will work very differently from a system developed for armored knights on the battlefield. Here it is important to look at both internal clues from the treatises being studied and external historical research concerning the forms of violent conflict that would likely be encountered by the target audience in the time and place the treatise was written.
Problem: How do we know whether we are interpreting the material in the treatises correctly? Are we following the steps correctly, using the right body mechanics? Are we missing important details which were left out of the written instruction? This is a difficult problem, especially for some of the older manuals which are far removed from modern pedagogy. The solution has pretty much been an exercise in widely distributed, open source, experimental archeology. In other words, a bunch of people around the world have spent the last few decades studying the manuals, coming up with ideas on what might have been meant, sparring with each other to discover how well those ideas work, then comparing notes, tweaking, adding, or discarding ideas, and then repeating the whole process over and over. Many practitioners have backgrounds in other systems which may help with insights (FMA, kenjutsu, kendo, modern Olympic fencing, etc), but those insights are tested against both practice and comparison to the historical texts.
Problem: Any sort of reasonably safe sparring or competition that we might use to validate our technique will necessarily have differences from actual application with deadly weapons. There are psychological differences (you behave differently when your life isn't really on the line). There are physical differences (a blunt training sword doesn't behave exactly like a sharp blade). How do we make sure we don't fall into the trap of, for example, creating a game of tag where competitors blithely run in to score a point with an ineffective tap while ignoring the likelihood of a lethal counterblow? There are a lot of possible ways to go wrong here, so there are a lot of potential solutions. For example, we can practice cutting objects with actual sharp reproduction swords and then work to make sure that our body mechanics for landing blows in sparring matches the body mechanics that we use for real cutting. We can experiment with sparring and tournament rules which reward behaviors which would be desirable in a real life or death fight. We can do experiments to discover how well certain historical weapons do or do not penetrate the historical armor of the time. Some advanced practitioners have experimented practicing partnered techniques with live blades, in order to better understand the "bind" which happens when edge-to-edge contact causes sword blades to "stick" to each other rather than sliding freely.
Problem: Certain weapons and fighting systems don't really lend themselves to any sort of reasonably safe sparring practice. Most HEMA practitioners work within systems that we can safely simulate with blunted training weapons and good protective gear - longsword, rapier, saber, or sword and buckler. That doesn't work so well for something like greatsword or cavalry vs infantry. In those cases we can drill the techniques from the manuals. We can do some exercises which should develop relevant skills. (For example, you can check out YouTube for the sport of "tent pegging", which is derived from the use of cavalry lance or sword against unmounted troops.) However we ultimately have to accept that we just can't develop the same degree of confidence in our skill or understanding of the technique for those systems.
Problem: Many, indeed most, martial systems and practices were never written down in the first place. (Or if they were, the manuscripts have been lost.) In this case we can examine the archeological and historical evidence - surviving artifacts (weapons and armor), artwork, remains with evidence of battle wounds, and then engage in "experimental archeology" to come up with potentially plausible theories on how those weapons might have been used. However, once again we have to accept that we really don't have a way to know how accurate those theories might be.
Bottom line: Drop bear asks "Is HEMA accurate?" Well, we have individuals who can fence with a blunted training sword with matches the weight and proportions of an historical sword, using techniques and principles laid out in historical manuals, and against 99+% of opponents they will be able to land what would be lethal blows without getting hit in return. These same individuals can also use sharp historical reproduction swords and cut through solid objects better than 99+% of the general public would be able to, using the same techniques and body mechanics. There are also a bunch of less talented practitioners studying the same historical texts, learning from the examples laid out by those leaders in the field, and testing ourselves with regular sparring and competition. Is it historically accurate? Well, in the absence of a time machine allowing us to go back and watch medieval fighters in person, we're working towards being as accurate as possible. The best we can do is check whether our practice matches the historical sources and whether it holds up to freestyle pressure testing.
