The diffraction of plane electromagnetic waves by apertures in a plane screen which is infinitesimally thin and perfectly conducting is studied both theoretically and experimentally. The theoretical analysis employs a dyadic Green's function to develop vector formulas for the scattered fields, and from these formulas integral equations are obtained for the aperture distributions. The vector representation makes possible a compact demonstration of the electromagnetic form of Babinet's principle by means of which one may extend the aperture analysis to complementary disks. The integral equations are then used to construct a variational principle for the aperture transmission coefficient.Detailed analysis and numerical computations are carried out for two configurations. For the circular aperture a first‐order vector trial function with frequency dependent coefficients is chosen for the aperture distribution. The approximate transmission coefficient is found to agree closely with the exact value in the region 2&pgr;a/&lgr;≤3. For elliptical apertures a zeroth‐order approximation is evaluated using a one‐component trial function. Numerical results are given for minor‐to‐major axis ratios of ½ and ⅓.Transmission coefficient measurements were carried out in the 24 000 megacycle band (&lgr;=1.25 cm) using an image plane technique. The apparatus was first calibrated with the exact solution of the circular aperture. The approximate results calculated for elliptical apertures are then seen to be in good agreement with the measurements over the accessible range.