I've always wanted to know this. If they had a likely spot, but it was too shallow would they try and dredge it? How? What was done to create ports and harbors before the advent of modern technology?
Great question, and thankfully a question which we have a good answer to.
We have a layman's guide to architecture written by the Roman architect Vitruvius. He just so happens to talk about the construction of harbors in Book 5, Chapter 12.
Ancients would rely mostly on natural features. A good shoreline with rocky spurs to block the weather. If these were not available, they could form a pier by heaping stones (you can see these all over the place at beaches). He talks about other ways to do this, like forming cement or stone walls.
He doesn't talk specifically about dredging, but from what he says about making piers, it seems reasonable to expect that they would make a temporary dam and dig out the silt. They dredged at Ostia, but it was considered a big deal, or else they wouldn't have bothered talking about it.
I've been thinking about this question and I think you may have a wrong impression. Cities did not generally make good ports and harbors. Rather good natural harbors generally lead to large and powerful cities. If the spot was too shallow dredging was generally impossible for any but the largest cities. Rome, Alexandria, Ephesus could all afford to dredge because they were large and powerful cities built largely by their harbors. Ephesus actually ceased to exist because it's harbor silted in. About 50 years before the city was abandoned a powerful earthquake damaged the infrastructure and led to a decline in population. The reduced population couldn't afford to dredge the harbor properly. It quickly silted in and the city was abandoned.