It is of both fundamental importance and practical value to measure the frequency of an LC resonator beyond the near-field region, especially when the resonator is used as a standalone capacitive sensor embedded inside a closed environment. To improve the coupling efficiency between the resonator and the external sniffer loop, we propose a novel method to integrate the LC resonator with a wirelessly-powered parametric resonator whose oscillation signal can be remotely identified in a noisy background. By measuring the minimum power level that is required for oscillation at different pumping frequencies, the resonator can be indirectly characterized by the frequency response curve. Starting from the basic principle of parametric oscillation, we will predict the measurable extremities in the frequency-dependent power curve under various circumstances that are classified based on the relative ratio between the lower and higher resonance frequencies. Our analytical models are validated by on-bench measurements performed on several parametric resonators with different circuit topologies. Their ability for remote characterization will make parametric resonators useful in structural health sensors or biomedical implants.