In this work, we carry out a study of gap and open-end discontinuities, using the ameliorated moment method which eliminates the spurious solutions in the calculation of eigenmodes. A rigorous solution for radiation and surface wave generation at high frequencies is obtained. Results are given for coupling and terminal capacitance and conductance, for the extended length versus the metallic strip width, the substrate thickness, the gap width, and versus the frequency for different values of permittivity. Our results, given here in the form of curves, are compared to other results obtained by quasi-static and full-wave methods, and to experimental results.