The pulsed electromagnetic (EM)-field propagation in configurations that are of relevance for the radiation from integrated antennas is examined. The investigated configurations consist of layered structures with material parameters that are typical for integrated circuits fabricated in complementary metal-oxide semiconductor technology, and are excited via small, conducting, current-carrying loops. Space-time expressions of the EM-field quantities are derived by using the modified Cagniard method. After validating it by means of comparisons with analytical results, the devised framework is used for examining the radiated field in the proximity of a chip. This study is instrumental for the analysis and design of close-range digital signal transfer.