Substrates having power 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 first power plane and a second power plane. The at least one noise suppression structure may include a first power plane extension that extends from the first power plane generally toward the second power plane, and a second power plane extension that extends from the second power plane generally toward the first power plane. Methods for suppressing noise in at least one of the first power plane and second power plane include providing such noise suppression structures between the power planes.