We consider the use of a resonant loop as a probe for the determination of roof thickness in a coal mine operation. The roof structure typically consists of a thin slab of uncut coal of the order of 10 cm in thickness, situated in front of a thicker layer of slate of relatively higher conductivity and permittivity. We model the structure by a two-layer half space, with the first layer consisting of a slightly lossy dielectric material (coal) and the second layer of infinite extent. To determine thickness of the bottom layer, i.e., the so-called roof, we propose that a horizontal loop be placed near the coal interface and the self-impedance of this loop be measured over a range of frequencies. The effectiveness of such a probing scheme is then determined, to a large extent, by our analytical ability to interpret such data in terms of the layer thickness. For a loop which is operating near its first resonance (where the cosinusoidal current is predominant), the measured change in the resonance characteristics provides additional information from which the layer parameters can be extracted. Such a remote sensor is relatively simple and presents no particular alignment problems.