Recently, there has been a growing interest in dielectric antennas and electromagnetic components based on periodic structures, since such components can be realized using new additive manufacturing technologies. The design of these components starts from the geometry of the unit cell, which determines not only the value of the effective refractive index but also the parameters of the entire considered component, like for example, the bandwidth of operation. For this reason, periodic structures with higher symmetry are of particular interest, since they can exhibit a wider bandwidth and other improved parameters. To analyze and design such components, we present a semi-analytical method for calculating the guiding properties of parallel-plate waveguides loaded with periodic glide-symmetric dielectric structures. It is shown that the presence of glide-symmetry can be simply included in the dispersion characteristic equation based on the transverse resonance condition.  The derived expressions reveal that due to glide-symmetry only the Bloch-Floquet modes of the same parity interact and contribute to the dispersion properties. The accuracy of the discussed method is verified through the analysis of several one-dimensional (1-D) and two-dimensional (2-D) structures suitable for the design of planar lens antennas with a large frequency band of operation.