Well, aside from the fact that they are described in ancient sources, we have archeological remains today of quite a few of these structures, which even if just a few foundation stones, at least tells us that there was at one point a very large building there. It is sometime possible to very roughly estimate the height of a ruined building from the size and depth of the foundations, since taller buildings, especially when made of masonry, require proportionally larger and deeper foundations.

Additionally, quite a few of these famous ancient monumental structures survived in to the medieval period. The Lighthouse of Alexandria, for example, remained in use as an active lighthouse, being maintained for that purpose, until it was damaged irreparably by a series of earthquakes in the early 14th century.