This paper presents an accurate integration method for computing Greenís function operators related to lossy conducting media. The presented approach is ultra-wideband i.e. the integration schemes cover the entire range of frequency behavior, from high frequencies where skin current is prevalent to low frequencies where volume current flow dominates. The scheme is a step towards permitting exact ultra-wideband frequency domain surface-only-based integral-equation simulation of arbitrarily-shaped 3D conductors, and towards obviating the need for volume-based explicit frequency-dependent skin effect modeling. This work deals specifically with the computation of Greenís functions and not with the unrelated but important low- frequency conditioning issue associated with the standard electric field integral equation.