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The method of steepest descents is applied to a parallel-plate waveguide where one of the plates is a bonded wire mesh modeled by a sheet impedance boundary condition. The structure is excited by a magnetic line source exterior to the waveguide. The parameters of the wire mesh are adjusted to exploit the contributions from the leaky-wave poles in the near far-zone radiation pattern. The use of the asymptotic expressions in this region is justified by comparisons with results obtained by numerical integration. The transient response of the structure is obtained by transforming the frequency domain response to the time domain with an FFT algorithm. An alternate representation for the magnetic field which is computationally efficient for determining the response in early time is derived. Numerical results for a double exponential pulse excitation of the line source are presented.