ASP Conference Proceedings, Vol. 340 (2005) p.455 One major problem of phase-referencing VLBI observations are phase errors due to the unknown tropospheric zenith delay at each antenna. These errors degrade the quality of the phase-referenced image and limit the achievable astrometric accuracy. We will present and compare two independent methods to estimate the zenith delay offset at each antenna. The zenith delay offsets can then be used to correct the data. These corrections improve the quality of the phase-referenced image and an astrometric accuracy of 10 $\mu$as can be achieved. With this accuracy, measurements of proper motions in the Local Group become feasible.