The radio frequency (RF) coupling to electronic devices impacts their EMC performance. The functionalities of a working electronic device may be disrupted when the electromagnetic (EM) coupling reaches a certain level. Studies of the EM coupling to printed circuit boards (PCBs) are therefore essential for RF susceptibility and EMC purposes. For decades, researchers focused on the analytical modeling of EM coupling to transmission lines. However, when it comes to more realistic PCBs the analysis usually still relies heavily on full-wave simulations because of the complexity of the structures and the lack of analytical solutions. Using a traditional full-wave modeling approach, however, could take hours to investigate the EM coupling from the external plane wave to the structure for one incident angle of arrival and polarization. In this paper, we present a methodology using reciprocity that allows for rapid estimation of the voltage induced in the terminations for multiple incident angles of the incoming plane wave and load values based on just one full-wave simulation. This reciprocity-based method is combined with a segmentation technique to enable the capability of studying the coupling to more realistic PCBs. For the cases studied here, estimates could be found in minutes using this approach rather than hours using a full-wave simulation. Estimates were within 2-3 dB of estimates using full-wave simulations for a simple trace structure. Accuracy was not as good for individual angles of arrival of an incident RF wave to a complicated structure including two integrated circuit (IC) packages connected by a trace, but statistical estimates of coupling were within 2-3 dB.