This paper describes numerical analyses of the distance-dependent gain variation that exists in gain measurements based on the Friis transmission formula for typical broadband antennas, including double-ridged guide horn and log-periodic dipole array antennas. The analyses are performed by simulating gain measurements using the method of moments with higher-order basis functions and the finite integration method. In addition, we propose approximate techniques to determine the antenna phase center by exploiting the distance dependence of the gain. Simulation and experimental results show the effectiveness of using the location of the phase center to accurately determine the far-field gain at reduced antenna separation distances.