We provide results of antenna radiation and total radiation efficiency at millimeter-wave frequencies gathered with a new open-ended waveguide-plate method that is compared to a well-known two-antenna method. The new method yields improved uncertainty in antenna efficiency measurements. Both methods are based on use of a reverberation chamber. Measurement results are compared to numerical simulations and good agreement (~3% maximum difference) is achieved. Before performing the efficiency measurements, the chamber configuration was assessed with respect to the Rician K-factor, number of uncorrelated paddle orientations, and coherence bandwidth. We calculated the uncertainty using the NIST microwave uncertainty framework capable of performing parallel sensitivity and Monte Carlo analyses. The framework enables us to capture and propagate the uncertainties in the S-parameter measurements to the final efficiency result. The expanded uncertainty that we achieved for these antenna efficiency measurements is 2.60%.