In some aspects, a resonator device for magnetic resonance applications is described. In some examples, the resonator device includes a resonator body that includes a periodic arrangement of cells about a central interior region. Each cell includes a dielectric substrate and a conductor disposed on the dielectric substrate. The periodic arrangement of the cells defines a periodic network of inductive and capacitive elements adapted to produce a magnetic field in the central interior region. The cells can be arranged according to various topologies that form various capacitive and inductive schemes. In some implementations, a dielectric substrate and thin superconductor are used, and the resonator device exhibits a high quality factor (Q) and low losses.