To better understand antenna properties in a narrow space such as in a densely-packed device, a circular microstrip antenna in a narrow parallel-plate waveguide is theoretically studied. An analytical expression is derived for the input impedance in a parallel-plate waveguide by using the cavity model with surface admittance on the side wall. The surface admittance is defined by the external magnetic field due to the equivalent magnetic current at the aperture and takes into account the contribution of the parallel plates to the antenna. The magnetic field external to the antenna, that is in the parallel-plate region, is determined by using a dyadic Green's function. The input impedance is then calculated by a basic definition based on the conservation of the complex power. An analytical expression which couples the resonant frequency and the surface susceptance is also formulated. Presented expressions are validated by comparison with experimental results.