Electromagnetic bandgap structures are considered a viable solution for the problem of switching noise in printed circuit boards and packages. Less attention, however, has been given to whether or not the introduction of EBGs affects the EMI potential of the circuit to couple unwanted energy to neighboring layers or interconnects. In this paper, we show that the bandgap of EBG structures, as generated using the Brillouin diagram, does not necessarily correspond to the suppression bandwidth typically generated usingS-parameters. We show that the reactive near fields radiating from openings within the EBG layers can be substantial and are present in the entire frequency band including propagating and nonpropagating mode regions. These fields decay fast with distance; however, they can couple significant energy to adjacent layers and to signal lines. The findings are validated using full-wave three-dimensional numerical simulation. Based on this work, design guidelines for EBG structures can be drawn to insure not only suppression of switching noise but also minimization of EMI and insuring signal integrity.