A theoretical estimate of the electromagnetic pulse from an extensive cosmic-ray air shower shows that the deflection of the electrons and positrons of the shower in the earth's magnetic field gives rise to a perturbed magnetic field with a forward traveling pulse whose momentum corresponds to that removed by the deflection of the charged particles. The angular divergence of this pulse is determined primarily by the curvature of the shower front corresponding to an angle of approximately 1/10 radian for low-altitude showers, increasing at greater altitude. The rise time is similarly limited by the structure of the shower front to approximately 10−8 seconds, but the decay time may be much longer because of the larger deflections at high altitude. Coincident optical radiation can be observed from the relatively wide-angle Cherenkov radiation from the sum total of the multiple-scattered shower electrons. Widely spaced optical detectors in coincidence must be used to discriminate against the more frequent lower energy single-particle or core Cherenkov events. Using these combined techniques, it is predicted that the highest energy cosmic-ray showers can be identified and their flux measured at angles nearly tangent to the earth's surface with a frequency greater than present counter arrays.