Extracting quantitative information from amplitude-modulation atomic force microscopy (AM-AFM) in viscous ionic liquids is difficult because existing theory requires knowledge of the cantilever natural frequency, which cannot be measured in the absence of a resonance peak. We present a new model that describes cantilever dynamics in an over-damped medium (Q < 0.5) and derive the theory necessary to extract the stiffness and damping in highly viscous liquids. The proposed methodology is used to measure the solvation layers of an ionic liquid at a gold electrode.