Single-degenerate massive binaries containing a black hole (OB+BH) are an important phase in the evolution towards BH mergers. Several OB+BHs were recently reported to exist on the basis of spectroscopic investigations. However, most of these reported OB+BH systems were later challenged by follow-up studies. This demonstrates the extreme difficulty to identify BHs using spectroscopic data alone. The recently published third Gaia data release (DR3) has provided us with the first Gaia astrometric orbits of binary systems. In preparation for DR3, we developed a unique method that uses Gaia astrometric orbital solutions for the identification of OB+BH systems. Assuming a direct collapse and no natal kick, an estimated 200 OB+BHs could be identified using the nominal Gaia precision. Moreover, we showed that different BH-formation scenarios could lead to distinct period and eccentricity distributions. However, we retrieved no astrometric OB+BH binaries in DR3. This poster describes our methodology for the identification of OB+BH binaries using Gaia astrometric binary solutions. I will demonstrate why the conservative publishing constraints imposed by the Gaia collaboration for DR3 led to a null detection, and how this can be remedied in the future.