Precise determination of antenna phase centers is crucial to reduce the uncertainty in gain when employing the three-antenna method, particularly when the range distances are short-such as a 3-m radio anechoic chamber, where the distance between the phase centers and the open ends of an aperture antenna (the most commonly-used reference) is not negligible compared with the propagation distance. An automatic system to determine the phase centers of aperture antennas in a radio anechoic chamber is developed. In addition, the absolute gain of horn antennas is evaluated using the three-antenna method. The phase centers of X-band pyramidal horns were found to migrate up to 18mm from the open end. Uncertainties in the gain were evaluated in accordance with ISO/IEC Guide 93-3: 2008. The 95% confidence interval of the horn antenna gain was reduced from 0.57 to 0.25dB, when using the phase center location instead of the open end. The phase centers, gains, polarization, and radiation patterns of space-borne antennas are measured: low and medium-gain X-band antennas for an ultra small deep space probe employing the polarization pattern method with use of the horn antenna. The 95% confidence interval in the antenna gain decreased from 0.74 to 0.47dB.