A superhydrophobic appliance is an elastomeric material with a surface having a multiplicity of re-entrant features. The elastomeric material can be a polydimethylsiloxane network. The superhydrophobic appliance can be formed by infusing a portion of a polydimethylsiloxane polymeric precursor partially into the pores of a porous membrane, curing to the polymeric network, and separating the membrane from the appliance to expose the superhydrophobic surface. The superhydrophobic surface can be subsequently modified to form a fluorinated surface that is oleophobic or superoleophobic in addition to being superhydrophobic.