Function
Antique swords are evaluated first from a purely functional perspective. Their creators didn't make them as museum pieces. They were tools of war, or at best ceremonial decorations worn during important occasions. Thus, practicality and functional use are good starting points for examining them. Assuming the weapon is in a state to be handled, you can grasp it by the hilt and carefully wield it the way its owner did. That helps you gauge the heft and the balance. Does the weapon fill you with confidence? How does its weight dictate the way you might swing it at an enemy? A personalized blade may have been fitted for a taller or a shorter user, or perhaps an older person who couldn't swing it as readily as a young man. Finally, the markings on the blade and elaboration of the hilt will speak to its overall purpose. Fancy designs and elaborate etching probably mean a ceremonial weapon, while plainer and more durable components speak to practical use on the field of battle. Ceremonial weapons are actually more common in antique sword collections because they were better preserved, and did not suffer damage from everyday use.
History
The construction of the weapon itself has a great deal to say about the technological advances of the culture which created it. It is often difficult to place the precise date that a sword was made, but evaluating its creation process can date it to within a century or so. Older swords are made of cruder grade steel, or simply forged from iron or bronze, while more advanced weapons used more complex alloys and improved purification techniques. More advanced isn't necessarily better in evaluating antique swords, and knowing the construction techniques can help you differentiate a forgery from the real thing. (Stainless steel probably means a replica weapon made in the twentieth century.)
Identification
Besides determining the age of the sword, forging techniques can signal which culture it came from. For example, western sword-making was often based around a single length of softer steel framed by an edge of firmer metal. This gave the weapon an amount of flexibility while allowing it to keep its shape. In Japan, on the other hand, makers of the famous katana created their weapons by folding the steel over and over again--achieving the same effect as their western counterparts through very different methods. Any existing symbols or hilt designs will help pinpoint the culture of origin as well, and master swordsmiths would often leave identifying marks as a signature of their work (though such marks could be falsified by subsequent smiths). Such clues can help pinpoint both when and where the sword was made, as well as determining what it might have been used for.(For example, high end swordsmiths likely worked for aristocrats or officers, not rank and file soldiers.
Expert Insight
Blades on antique swords served three essential functions: guarding (defense), binding (catching or locking the enemy's weapon) and striking (attack). Its effectiveness in these categories--and therefore its use--can be determined by examining the length and heft of the blade, as well as testing its flexibility and balance. A thin pointed blade, for example, likely served for duels of honor, where the intent was to draw blood but not necessarily harm an opponent. The length and size of the blade also help determine its formal category: rapier, broadsword, falchion, saber, cutlass and so on. Nicks and marks along the blade reveal how often it was used and what kind of fighting it saw, though one must take care to differentiate the wear and tear of regular use with corrosion and decay caused by time.
Expert Insight
So too does the hilt of the sword deliver insight into its type and use. If the hilt doesn't match the style and age of the blade, it will likely repaired at some point (or else is a fake). The firmness of the grip can tell you the purpose for which the sword was used, and the style of fighting can be partially deduced through the basket or pommel guard on the hilt. Many of these things cannot be evaluated without the hilt--if you cannot grasp the sword, it's tougher to get a feel for how it plays--and copies or forgeries will pay less attention to details, such as the thickness of the tang, than genuine antique swords will.