A dual-mode resonator comprises a dielectric substrate having a region divided into four quadrants, and a ring resonator forming quadrangularly symmetrical configurations within the four quadrants of the region. The symmetrical configurations may be formed from folded sections of the resonator, so that parallel lines with opposite currents that cancel to minimize the far-field radiation of the filter structures. The symmetrical configuration can also be meandered, so that opposite currents in parallel line segments within each meander and the line segments that interconnect the meanders cancel to minimize the far-field radiation of the filter structures. One resonator can be used in a two-pole dual-mode filter structures, or multiple resonators can be used in more complex dual-mode filter structures. The filter structures also include input and output couplings with capacitors and transmission lines that directly connected to the resonator to provide a point of contact, which more accurately represent ideal lumped element capacitor connections from computer modeling.