The best I can do to summarise the complex subject of secular Sea Level Rise (SLR) is to start with Wikipedia (note that here, we define time as BP-Before Present, i.e. with a 2000 year shift compared to BC):
“eustatic sea level has fluctuated significantly over the earth’s history. The main factors affecting sea level are the amount and volume of available water and the shape and volume of the ocean basins. The primary influences on water volume are the temperature of the seawater, which affects density, and the amounts of water retained in other reservoirs like rivers, aquifers, lakes, glaciers, polar ice caps and sea ice. Over geological timescales, changes in the shape of the oceanic basins and in land/sea distribution affect sea level. In addition to eustatic changes, local changes in sea level are caused by tectonic uplift and subsidence.”
It is obviously difficult to differentiate eustatic SLR from crustal movements of the earth as our measuring instruments are placed on the earth. The best approach is to assess that water is supposed to remain ‘horizontal’ on a large basin like the Mediterranean Sea, while crustal movements occur at a more local scale (e.g. Crete). Hence, the average of all measured sea level movements on the entire basin will reflect the eustatic SLR, while local deviations from this average will reflect the local crust movements.
Many studies were conducted in recent decades to evaluate past eustatic SLR and to predict future eustatic SLR for the next century(s). The best known is the work of Kevin Fleming (1998). To make it short, the results are as follows, in round figures:
- Predicted for the 21st c.: around 5 to 10 mm/year, and more
depending on prediction model used;
- Observed in the 20th c.: around 2 mm/year;
- Observed in the past 2 000 years: around 0.25 mm/year,
resulting in ca. 0.50 m eustatic SLR over this period;
- Observed between 7 000 and 2000 BP: around 0.7 mm/year,
resulting in ca. 3.50 m eustatic SLR over this period;
- Observed between 15 000 and 7 000 BP: around 14 mm/year,
resulting in ca. 110 m eustatic SLR over this period.
Since the rise of human civilisations around 7 000 BP, eustatic SLR has been around 4 m. This value must obviously be combined with local crustal movements which may have reached several meters uplift (e.g. Phalasarna) or subsidence (e.g. Alexandria, Apollonia Cyrenaica, Portus Iulius, Rome, and many others) and sometimes both (Pozzuoli).
As an example, let’s take the area of Rome which has been studied in detail over a period of 2 000 years by Goiran (2009) based on an analysis of marine shells, and by Lambeck (2018) based on an analysis of coastal fish tanks. The first conclude with a relative SLR of 0.8 m, and the latter with 1.22 m, hence both are quite close to 1.0 m. This relative SLR is thus composed of 0.5 m eustatic SLR + 0.5 m crustal subsidence.
Another interesting case is given by Morhange (2014) who shows that the relative SLR of 0.5 m in 2 000 years in Marseille-La Ciotat-Fréjus equals the eustatic SLR because no significant crustal movements occurred in this area during several millennia.
A more controversial case is the Black Sea. It is accepted that it was once a fresh-water lake disconnected from the Mediterranean Sea by a sill in the Bosphorus located around -36 m below present sea level (deepest spot of the shallowest cross-section in the Bosphorus located in front of Dolmabahçe Palace).
This configuration existed until around 9000 BP when, due to global eustatic SLR, Mediterranean water started to flow over the sill into the Black Sea-lake. The questions are: how deep was the lake water level at that time, and how fast did the water level rise? Even if the lake water level was much deeper than the Bosphorus sill, e.g. -80 to -100 m acc. to Yanchilina (2017), flooding must have been rather progressive because, as mentioned above, global SLR was around 14 mm/year … unless the sill in the Bosphorus collapsed, perhaps during an earthquake.
In any case, scholars agree on the fact that after reconnection with the Mediterranean Sea, the Black Sea water level followed the global eustatic SLR. This means that Neolithic and Bronze Age settlements were not affected by the controversy about the Black Sea water levels, i.e, Neolithic settlements dated around 6000-3000 BC might be found between 15 and 2 m depth below the present sea level.
 Flemming, N.C., Webb, C.O., 1986, “Tectonic and eustatic coastal changes during the last 10,000 years derived from archaeological data”, Z. Geomorphol. Suppl. 62, (p 1–29).
Flemming, N.C., Czartoryska, N.M.G., Hunter, P.M., 1973, “Archaeological evidence for eustatic and tectonic components of relative sea level in the South Aegean”, 23rd Symposium of the Colston Research Society, Bristol, 1971, Pap. 23, (p 1-63).
 Morhange, C., 2014, “Ports antiques et variations relatives du niveau marin”, Géochronique n°130, (p 21-24).
 Fleming, K., et al., 1998, “Refining the eustatic sea-level curve since the Last Glacial Maximum using far- and intermediate-field sites”, Earth and Planetary Science Letters 163, (p 327–342).
 Goiran, J-P., Tronchère, H., Collalelli, U., Salomon, F., Djerbi, H., 2009, “Découverte d’un niveau marin biologique sur les quais de Portus : le port antique de Rome”, Revue Méditerranée, 112 | 2009, (online), (10 p).
 Lambeck, K., Anzidei, M., Antonioli, F., Benini, A., Verrubbi, V., 2018, “Tyrrhenian sea level at 2000 BP: evidence from Roman age fish tanks and their geological calibration”, Rendiconti Lincei. Scienze Fisiche e Naturali, Satellite Geodetic Positioning for Geosciences, Roma, 2017, (12 p).
 Yanchilina, A., et al., 2017, « Compilation of geophysical, geochronological, and geochemical evidence indicates a rapid Mediterranean-derived submergence of the Black Sea’s shelf and subsequent substantial salinification in the early Holocene », Marine Geology, 383 (2017), (p 14-34).
 A simple hydraulic computation with a sill at -36 m shows that this global SLR would induce a rise of the Black Sea level (from -90 m) within around 200 years, inducing a gradually increasing SLR in the Black Sea not exceeding 1 m/year. This is fast, but it is not a catastrophic flood. The « deluge hypothesis » can only be explained by collapse of (a part of) the Bosphorus sill.
 Gökaşan, E., et al., 2005, « Evidence and implications of massive erosion along the Strait of Istanbul (Bosphorus) », Geo-Mar. Lett. 25, p 324–342.