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A simple analytical model to predict bounding estimates of shielding effectiveness of realistic complex resonant cavities is presented. The model is based on knowledge of the transmission cross section of the apertures, and the volume and the quality factor of the cavity. The average shielding effectiveness is given by an analytical expression and the upper bound is found using a statistical approach. The statistics are found by assuming the internal field conditions to be similar to those inside a reverberation chamber. A very good agreement is found between model predictions and measured data.