Overmoded-waveguide method (OWM) can effectively alleviate the errors caused by air gaps in waveguide measurements of dielectric properties. In our previous study, both sides of the standard waveguides are enlarged by a same factor (bilateral-OWM). However, as frequency increases to sub-terahertz and terahertz bands, bilateral-OWM will inevitably introduce resonant peaks, which will increase the uncertainty. Therefore, we proposed the unilateral-OWM, which can effectively reduce the occurrence of resonant peaks and improve the measurement accuracy. To verify the feasibility of this method, polytetrafluoroethylene (PTFE) is simulated and measured with bilaterial- and unilateral-OWMs, respectively. Simulation shows that with an overmoded factor of 3.94 and air gap of 0.08 mm, the value of the relative error of εr is basically the same in bilateral- and unilateral-OWMs, but the uncertainty of εr is 0.06% in the bilateral-OWM and 0.01% in the unilateral-OWM. [ABSTRACT FROM AUTHOR]