From a EurkekAlert press release giving abstracts of the latest issue of Geology:

Young Danube delta documents stable Black Sea level since the middle Holocene: Morphodynamic, paleogeographic, and archaeological implications

Liviu Giosan, Woods Hole Oceanographic Institution, Geology and Geophysics, Woods Hole, Massachusetts 02543; et al. Pages 757-760.

Sea level in the Black Sea has long been controversial, at a variety of time scales. Sea level curves from the region show large magnitude (up to 15 meters) and high frequency level variations since the early Holocene despite the fact that the Black Sea was already connected to the World Ocean. A new chronology for beach ridges in the Danube delta -based on mass spectrometry radiocarbon measurements and supported by optically stimulated luminescence dates - shows that the Black Sea water level remained within -2 m and +1.5 m of the current level for the last five millennia. Hydroisostatic effects related to a catastrophic reconnection of the Black Sea to the World Ocean in the early Holocene may have played a role in reaching the Holocene highstand earlier than estimated by models. The new dates also demonstrate that the Holocene Danube delta started to build out of a Black Sea embayment only ~5200 years ago, rather than ~9000 years ago as previously proposed. The new chronology allows for a better understanding of the Danube delta paleogeography, including the demise of Histria, the main ancient Greek-Roman city in the region, whose harbor has been shoaled with sands transported alongshore from the updrift Danube coast. Further, submergence at several ancient Chalcolithic/Bronze Age to Greek-Roman settlements along the Black Sea coast may be better explained by local factors such as subsidence, rather than by basin-wide sea level fluctuations.

There's a fairly good website for the ongoing excavations at Histria ...