That's the correct term, I hope? My question concerns swords with hilts consisting of several bars and rings joined together, such as swept hilt rapiers, side-swords, certain hand-and-a-half swords, etc.

Basically, how were these hilts made historically? Where they cast, or welded? And how are they typically made today for reproductions?

Hello,
Check this link http://www.templ.net/english/making-hilts.php
You may find it interesting, however the maker does not let out much of his technic. In my oppinion that is the historical method.

I have looked into this myself and discussed it with those who have handled and studied originals, mainly concerning British basket hilts. They appear to have been forge-welded in many cases, although some designs could be and were made by piercing and forming flat sheet, and brazed joints are not unknown either. Brazed joints are often seen on repairs. Riveted joints were used occasionally but usually only on selected joints on any particular hilt. Attatching the "cup" to a cup-hilt rapier is an example of a common rivet joint. Later pieces may have screws in place of rivets.

Thanks for the info, both of you. :)

Forge welding, huh? Is that more advantageous to regular welding, somehow? Or could the same results be achieved with electrical or gas welding methods?

I think what Peter said about the skill and care of the welder being the major factor is correct. Another difference with a forge weld however is that if done cleanly, with no impurities in the joint, it forms a totally homogenous joint. Modern welding methods generally use a filler wire, stick or rod which may be similar in alloy/content but will rarely if ever be identical to the parent pieces so in the weld itself you have a steel that is dissimilar to some degree. If the weld is done properly for the application it should not be weaker than the parent material but some processes such as heat treating or machining can be affected by the difference in the weld material. For hilts this is probably disregardable, although the weld may age differently than the parent material.
Historically I think most forge-welded hilts were made of wrought iron which is supposedly easier to forge weld than most modern steels.

One other worth while aspect of the welding method;
When comparing results from highly skilled craftsmen who are fully competent with the respective methods, forge welded joints are undeniably more beautiful and flowing as if the entire guard were somehow miraculously constructed out of a single piece of metal that was perfectly split and formed. I have excellent welders at my work who are competent with Arc, TIG, MIG, gas torch, etc. Despite 20+ year careers of full time welding, what they produce does not compare visually with the forge welded work we see in some authentic-historical sword guards.

Forge welding is unique and more better than modern welding methods. It is more difficult to learn and there are danger (defect). Patrik Barta work with wery old iron (knobbled iron? from baroque garden). Process forge welding of the renaissance handel (and other smoll objects) hanging by fast work and one good hammer blow. Bad, late, bad location hammer blow can destroyed weld.
And is not truth that all current materials are not good to forge welding. It is possible to welding iron and cast iron and some alloy steel. In this case is important use to welding mediums (fullers earth, sand, file dust....).