Back-slung scabbards are mostly fictional, for sure. While there might be some rare examples, there doesn't seem to be any example of them being standard or common practise.

To keep this short, the essential answer is that there was no personal storage for dedicated two-handed swords. They would be carried into battle, and if a different weapon was required, they'd often simply be dropped. Two-handed swords too large to be worn at the hip were the exception, though. During the late Middle Ages and the Renaissance (c.1200-1600), the overwhelming majority of two-handed swords were relatively lightweight compared to popular conception, often coming in at 3lbs (or around 1.8kg). Even heavier examples of such swords can be used one-handed, in a limited and temporary fashion, while some two-handers were basically a one-handed sword blade mounted in an elongated hilt. In modern study of this kind of sword, it's considered widely appropriate to call these "longswords", "bastard swords" or "hand-and-a-half swords". So two-handed swords were generally not two-handed in an absolute sense, but were preferable to use in two hands. They were built for versatility, and could be worn at the hip. This allowed them to be taken into battle in addition to a weapon carried in one's hands, such as a lance if on horseback, or a poleaxe. In a civilian context, such swords were very convenient, although many civilians appear to have preferred the sword & buckler combination.

Such swords appear commonly from c.1250 to c.1550, with fringe use on either side. I believe the last manual written in premodern times for two-handed swords is attributed to the 18th century and is, unsurprisingly, of German origin. I might have to check that up, though, as my knowledge of any later manual that isn't by Joachim Meyer is a tad thin. In any case, the essential answer is that especially large two-handed swords were carried into battle in one's hands. If the weapon became inconvenient, a warrior had little recourse but to drop it. Such large swords were the exception, though, even among other two-handed swords, which tended to be more broadly ergonomic and more versatile in a variety of different roles.