Radio and microwave sensing and imaging technologies are attractive for applications where traditional techniques require an invasive operation or that the patient be exposed to harmful ionizing radiation, as in an x-ray or computed tomography scan. Radio and microwaves have a wavelength long enough that it cannot ionize atoms in the body, making it safer than x-ray techniques while still penetrating through tissue. Recently, a flexible and wearable electromagnetic resonator sensor in the form of a single-arm Archimedian spiral wirelessly powered by a coplanar loop antenna has emerged as a promising design for noninvasively monitoring a variety of physiological parameters like heart rate, left ventricular stroke volume from the heart, and intracranial pressure. These spirals have multiple resonant frequencies in the radio and microwave frequency range that are modulated by the electrical properties of the tissue around it. Thus, a shift in resonant frequency is believed to correspond to physiological changes in the body by altering its effective electrical properties. In this thesis, two successful resonator designs, a square and circular spiral, are modeled, simulated, and analyzed using computational electromagnetics software. Analyses performed include characterization of the radiation patterns of the resonator, a specific absorption rate study to evaluate the amount of energy absorbed by the body from exposure to radiation emitted from the resonator, and a validation of the suspected operating principle of the resonators in two biomedical applications: arterial pulse detection and intracranial hemorrhage detection. Finally, the use of a spiral resonator for imaging applications is briefly investigated.