Abstract: Novel structures and methods for forming useful high temperature superconducting devices, most particularly resonators, are provided. Structures resulting in reduced peak current densities relative to known structures achieve numerous desirable benefits, especially including the reduced intermodulation effects of earlier resonators. In one aspect of this invention, a spiral in, spiral out resonator is provided, characterized in that it has an odd number of long runs, at least equal to five long runs, where the long runs are connected by turns, and wherein there are at least two sequential turns of the same handedness, followed by at least two turns of the opposite handedness. In yet another aspect of this invention, it has been discovered that reducing the size of the input and output pads of HTS resonators increases the relative inductance compared to the capacitance. Yet another resonator structure is a spiral snake resonator having a terminal end disposed within the resonator.