A resonator of a planar circuit type is provided for receiving a signal from an input end and transmitting a signal to an output end. The resonator includes: (a) a dielectric substrate; (b) a ground plane including a layer of conductive material formed on the bottom surface of the substrate; (c) an inductor formed on the top surface of the substrate and connected to the input and output ends; and (d) a series capacitor connected in parallel to the inductor, wherein the series capacitor includes two patches of conductive material formed on the top surface of the substrate, each patch being connected to one respective end of the resonator. Each patch also forms a shunt capacitor with the ground plane, and the capacitance of the shunt capacitor constitutes the majority of capacitance between the ground plane and the end of the resonator that is connected to the patch. The conductive material may be a superconductor, including oxide superconductors. Filters utilizing multiple resonators of the invention are also described. The integration of the series and shunt capacitors results in a more compact resonator and filter layout, allows broader manufacturing tolerances, and allows for more layout flexibility than is attainable with the technology of the prior art.