Substrates having power and ground planes, such as, for example, printed circuit boards, include at least one noise suppression structure configured to suppress electrical waves propagating through at least one of a power plane and a ground plane. The at least one noise suppression structure may include a power plane extension that extends from the power plane generally toward the ground plane, and a ground plane extension that extends from the ground plane generally toward the power plane. The ground plane extension may be separated from the power plane extension by a distance that is less than the distance separating the power and ground planes. Electronic device assemblies and systems include such substrates. Methods for suppressing noise in at least one of a power plane and a ground plane include providing such noise suppression structures between power and ground planes.