I'd defer to European scholars on this, or even fencing experts, but it seems pretty ludicrous to me that if you could wield a sword capably with one hand, that you'd use the other to brandish yet another sword. A shield seems like a much safer bet, or even a dagger (as I've seen in some fencing texts), as it would allow a person to parry or block a strike much more effectively in concert with offensive sword strikes. Presumably the second sword would increase a person's offensive capability (if the purpose was defensive, why not use a shield?), but could that ever really be the case? I know different kinds of swords are used differently (and some swords actually work better in application if wielded with both hands), but is the dual-wielding sword thing you sometimes see in movies just that, a Hollywood creation with no basis in history? Is there any historical evidence of a person using two swords in combat or a duel?
You only mentioned Western fencing in the OP- but it’s worth noting that the classical Japanese martial art Hyōhō Niten Ichi-ryū is generally considered to be an at least somewhat authentic transmission of the teachings of the 16th century samurai Miyamoto Musashi, since it’s listed in the authoritative Bugei Ryuha Daijiten. It is chiefly known for its technical material concerning the simultaneous use of two swords, though it also teaches the katana used alone, the staff, and a type of policeman’s truncheon known as the jutte.
This can at least partially be attributed to the fact that it was traditional for the samurai of Musashi’s day to routinely wear a paired long and short sword as badges of their status- so while they might have wished to have a shield or dagger, they knew that a pair of swords would be at hand, and so trained with what would be readily available.
I'm not aware of any accounts of duels using two swords - but accounts of duels are surprisingly not that common. The accounts I've come across are generally about the social consequences and not the technical or tactical details.
Starting in the late 16th century, there was a profusion of a sort of "how to" fencing manual. [A number of these include etchings] (https://qph.ec.quoracdn.net/main-qimg-4cb7f9432f24cb182543e011fd51f072) and discussions of using two swords. In English, this was sometimes called a "case" of swords.
I have no idea if this was an intellectual exercise, a boast about skill and artistry, or earnest instruction for swordfights.
I just came across this and thought you might be interested. It's a discussion of a military treatise from 1603, written up by somebody practicing historical fencing.
Cassani predominantly describes passing footwork, and exclusively employs cuts, quite unlike any comparable Italian work from the first decade of the seventeenth century. It is also of interest that in the few pages he dedicates to fencing, he discusses combat with two swords, like Altoni, Docciolini, and Palladini, 2 recommending a second sword as the first companion arm to be learned before other combinations.
On "La Verdadera Destreza" the Spanish Empire fencing style promoted the use of the parrying daggers called "Vizcaina", they had teeth like saws, so they could drag after parry. It also address the importance of the short blade, based on the geometrical principles, you can repel the point of a long sword with a dagger using much less force. Think also on better aiming, to find the vulnerable spots thru the armors, as well as speed. If the situation turns into close quarters the dagger also offers better options.
About the shield, take a look on the latest rapier sword styles, they have a full cover for the hand with the porpuse of replacing the shield, they called that "cazoleta".
Seems like it worked well for the Tercios.