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With the proliferation of small electric devices in recent years, along with various other applications, there is a growing need to test and determine the shielding properties or shielding effectiveness (SE) of physically small (but electrically large) enclosures or cavities. In this paper, we discuss how a reverberation chamber technique can be used to measure the SE of such enclosures. The approach consists of placing the small enclosure inside a reverberation chamber and using frequency stirring to excite the reverberation chamber. A small surface probe (i.e., a monopole) is mounted on the inside wall of the small enclosure to measure the power level inside the small enclosure. We present measured data from various other reverberation chamber approaches obtained from various enclosure configurations. The data from these other reverberation chamber approaches are used to validate the proposed approach. We also compared measured data to theoretical calculations of the SE for two small enclosures with circular apertures. These various comparisons illustrate that the proposed technique is a valid approach for determining the SE of physically small (i.e., cubic enclosure dimensions of the order of 0.1 m and smaller), but electrically large enclosures (that support several modes at the lowest frequency of interest).