We present a suite of gravitationally self-consistent predictions of sea-level change since Last Glacial Maximum (LGM) in the vicinity of the Bosphorus and Dardanelles straits that combine signals associated with glacial isostatic adjustment (GIA) and the flooding of the Black Sea. Our predictions are tuned to fit a relative sea level (RSL) record at the island of Samothrace in the north Aegean Sea and they include realistic 3-D variations in viscoelastic structure, including lateral variations in mantle viscosity and the elastic thickness of the lithosphere, as well as weak plate boundary zones. We demonstrate that 3-D Earth structure and the magnitude of the flood event (which depends on the pre-flood level of the lake) both have significant impact on the predicted RSL change at the location of the Bosphorus sill, and therefore on the inferred timing of the marine incursion. We summarize our results in a plot showing the predicted RSL change at the Bosphorus sill as a function of the timing of the flood event for different flood magnitudes up to 100 m. These results suggest, for example, that a flood event at 9 ka implies that the elevation of the sill was lowered through erosion by ∼14–21 m during, and after, the flood. In contrast, a flood event at 7 ka suggests erosion of ∼24–31 m at the sill since the flood. More generally, our results will be useful for future research aimed at constraining the details of this controversial, and widely debated geological event.