We present a full wave theoretical model for an induction gradiometric sensor employed for detection of conductivity contrast. The sensor is composed of a wire antenna radiating from a rectangular waveguide, with receivers in the waveguide positioned symmetrically on either side of the transmitter. We first solve the canonical problem of an open-ended rectangular waveguide in a planar stratified medium and then apply reciprocity and the Born approximation to deduce the response of the sensor in the presence of an arbitrary external medium. We compare our results against experimentally measured data and find excellent agreement. We present a discussion of these results together with an analysis of the numerical considerations involved in the computation.