Many harbors after the fall of Rome were either abandoned because they silted up, or had to move because the coast eventually moved out to sea and the original location was now far inland. In some cases they ended up miles away from the ocean after a few centuries. Clearly it was a costly and labor intensive task or else post roman societies would have continued it. I believe it involved some sort of boat with an "arm" of some sort to dig up the sediment, but I have not come across any detailed explanation of how exactly romans would remove thousands of square feet of mud from the bottom of the harbor?
This is an interesting question, and this thread is a wasteland of deleted replies. I've been doing a bit of looking around and I am not finding very much discussion of the hows. Vitruvius, in his de architectura, mentions in passing the operations to dredge harbors at several cities in Asia Minor (on the modern western coast of Turkey). We know that due to geomorphological, hydrological, and human-influenced factors, these harbors were "silting" rapidly at the end of antiquity, and in fact today are in some cases now several miles inland. At Ephesus in particular, the Romans seem to have fought a stubborn but futile battle against the silt. There are a lot of technical stratigraphic studies of ancient dredging attempts, in Asia Minor and also in Marseilles and at the mouth of the Tiber, for example. This paper, which is all over the internet and clogs up searches, is a good example of the kind of scientific work that can be done on the question of dredging. Figure 8 in that paper shows the remains of an ancient ship, 1st or 2nd century CE, which most agree had something to do with dredging operations. It has a central "well" (hole) in the bottom of the hull through which the "arm" of dredging machinery passed. I am not at all an expert on how the engineering would have worked. Their figure 9 shows how it was done almost two millennia later, if that's any help. The technical papers all show plainly that the dredging operations were extensive in the Roman Imperial period in several key cities; we just don't have good evidence to say more in this case, at least not as far as I can find.
I also found this thread from four years ago that talks about dredging. /u/iwinagin talks with some better authority than I can muster on the different methods.
Do you have any examples of these inland ports? I'd love to check them out on google maps :)