A planar epsilon-near-zero (ENZ) tunnel structure implemented on substrate integrated waveguide (SIW) technology is used to evaluate the complex dielectric permittivity of various materials. Design, optimization, and fabrication of the ENZ tunnel structure are explained. Simulations and measurements on various dielectric samples using the cavity perturbation technique of the proposed structure are presented. Measured values of the permittivity are in good agreement with standard values. Sensitivity analyses are performed on the ENZ structure and the conventional SIW cavity techniques. The proposed structure has very high sensitivity, which yields more accurate results when compared to other techniques, such as perturbation of conventional cavities.