Numerical analysis of the electromagnetic radiation from conducting surface structures is concerned. The method of moments is discussed with the surface-patch modeling in which the surface quantities, i.e. the current, charge and impedance are directly introduced and with the wire-grid modeling in which the surface quantities are approximated by the filamentary traces. The crucial element to a numerical advantage of the wire-grid modeling lies in the simplicity of its mathematical involvements that should be traded for the uncertainties in the construction of the model. The surface-patch techniques are generally not only clear and straightforward but also more reliable than the wire-grid modeling for the computation of the surface quantities. In this work, we bring about a comparative discussion of the two approaches while the analysis of a built-in planar antenna is reported. For the purpose of the comparison, the same electric field integral equation and the Galerkin's procedure with the linear expansion/testing functions are used for both the wire-grid and surface-patch modeling.