The work considers the analysis of antenna and arrays of thin wires of arbitrary orientation above imperfectly conducting ground planes. Emphasis is placed on the development of fast and accurate techniques for computation of the characteristics of antenna systems. An important problem is the evaluation of certain semi-infinite integrals encountered in the exact Sommerfeld solution. The time required for computation of these integrals is reduced by the application of interpolatory quadrature formulas. Where applicable, a modified method of steepest descent is used to evaluate the integrals. The approximate reflection coefficient method is derived from the Sommerfeld formulation via the method of steepest descent. The accuracy of the reflection coefficient method relative to the Sommerfeld method is discussed. Finally, formulas convenient for the optimization of various performance indices are discussed. Typical indices that have been optimized, both with and without constraints, are directivity, power gain, quality factor, and main beam radiation efficiency.