The EDGES High-Band experiment aims to detect the sky-average brightness temperature of the 21 cm signal from the epoch of reionization in the redshift range z 14.8 6.5. To probe this redshifted signal, EDGES High-Band conducts single-antenna measurements in the frequency range MHz from the Murchison Radio-astronomy Observatory in Western Australia. In this paper, we describe the current strategy for calibration of the EDGES High-Band receiver and report calibration results for the instrument used in the 2015-2016 observational campaign. We propagate uncertainties in the receiver calibration measurements to the antenna temperature using a Monte Carlo approach. We define a performance objective of 1 mK residual rms after modeling foreground subtraction from a fiducial temperature spectrum using a five-term polynomial. Most of the calibration uncertainties yield residuals of 1 mK or less at 95% confidence. However, current uncertainties in the antenna and receiver reflection coefficients can lead to residuals of up to 20 mK even in low-foreground sky regions. These dominant residuals could be reduced by (1) improving the accuracy in reflection measurements, especially their phase, (2) improving the impedance match at the antenna-receiver interface, and (3) decreasing the changes with frequency of the antenna reflection phase.