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We have modeled, fabricated, and characterized superhydrophobic surfaces with a morphology formed of periodic microstructures which are cavities. This surface morphology is the inverse of that generally reported in the literature when the surface is formed of pillars or protrusions, and has the advantage that when immersed in water the confined air inside the cavities tends to expel the invading water. This differs from the case of a surface morphology formed of pillars or protrusions, for which water can penetrate irreversibly among the microstructures, necessitating complete drying of the surface in order to again recover its superhydrophobic character. We have developed a theoretical model that allows calculation of the microcavity dimensions needed to obtain superhydrophobic surfaces composed of patterns of such microcavities, and that provides estimates of the advancing and receding contact angle as a function of microcavity parameters. The model predicts that the cavity aspect ratio (depth-to-diameter ratio) can be much less than unity, indicating that the microcavities do not need to be deep in order to obtain a surface with enhanced superhydrophobic character. Specific microcavity patterns have been fabricated in polydimethylsiloxane and characterized by scanning electron microscopy, atomic force microscopy, and contact angle measurements. The measured advancing and receding contact angles are in good agreement with the predictions of the model.