A contactless method based on reflectometry to accurately characterize an inductive radio frequency (rf) resonator even in the occurrence of a strong electrical nonlinearity is presented. Nonlinear extraction of the unloaded quality factor and resonance frequency is possible by combining an initial low-level swept-frequency calibration with high-level single-frequency measurements. The extraction protocol relies on a simple intrinsic R, L, C model and does not involve a fitting procedure according to a particular nonlinearity model. It includes a correction for strong coupling conditions between the probe and the rf coil, which allows extending the analysis over a wide range of transmitted power. Electrical modeling based on the extracted intrinsic data allows predicting the coil behavior when loaded by any kind of matching network. The method will have implications in different domains such as Magnetic Resonance (MR) applications with superconducting probe heads or analysis of rf properties in nonlinear materials. The method is demonstrated here by characterizing a high temperature superconducting (HTS) coil dedicated to MR imaging at 64 MHz. The coil consists in a multiturn spiral design that is self-resonant close to the MR frequency of interest. The Q factor and the resonance frequency are determined as a function of the actual power dissipated in the HTS coil accounting for losses occurring in the measurement system. Further characteristics of the HTS coil are considered in the present paper. The relation between the transmitted power and the magnetic field generated by the coil, which is the most relevant characteristics for MR applications, is directly accessible. The equivalent impedance of the coil under test is also expressed as a function of the total current flowing in the windings. The method could be extended to assess the fundamental properties of the nonlinear material (e.g., the London penetration depth or the critical current density) by including any pertinent model.