Printed leaky-wave antennas offer the potential for a low-profile, wide-bandwidth antenna element that can be arrayed if desired. Microstrip leaky-wave antennas rely on the suppression of the familiar EH₀ mode and the propagation of the radiating EH₁ mode. It is well-known that above a critical frequency, this leaky-wave will propagate with little attenuation and that the phase difference between the two radiating edges of the microstrip leads to radiation. However, due to the limits of installation area, such antennas must be terminated in a manner that reduces back reflection. If this is not done, a standing wave is established on the antenna limiting its utility as a leaky-wave antenna in terms of front-to-back ratio and bandwidth. In this paper, the hybrid finite element-boundary integral method is used to investigate an antenna termination scheme involving the use of resistive sheet extensions to the antenna. It was shown that such a termination increases the front-to-back ratio and usable bandwidth of the antenna as compared to an antenna without such termination.