Distributed antennas must be phase-calibrated (phase-synchronized) for certain operations, such as reciprocity-based joint coherent downlink beamforming, to work. We use rigorous signal processing tools to analyze the accuracy of calibration protocols that are based on over-the-air measurements between antennas, with a focus on scalability aspects for large systems. We show that (i) for some who-measures-on-whom topologies, the errors in the calibration process are unbounded when the network grows; and (ii) despite that conclusion, it is optimal -- irrespective of the topology -- to solve a single calibration problem for the entire system and use the result everywhere to support the beamforming. The analyses are exemplified by investigating specific topologies, including lines, rings, and two-dimensional surfaces.