Stellar-mass black holes have been detected by radial-velocity observations in star/black hole binaries .
These allow only the determination of the mass function .
Tracking the astrometric orbits of the visible components of the star/black hole binaries would allow the full determination of the black hole masses , which would be of great astrophysical interest .
We investigate the possibilities to do this with Gaia .
A very promising object seems to be Cyg X-1 .
The donor star is an O9.7Iab supergiant having a mass of 25 M _ { \odot } , and the mass of the black hole is estimated to be at least 13 M _ { \odot } masses .
The period of 5.6 days implies a semi-major axis of 1.01 \mu pc of the binary orbit .
At the distance of Cyg X-1 ( 2.5kpc ) this translates into a semi-major axis of about 28 \mu arcsec for the visible component , which can be detected by Gaia .
We discuss further candidates .