An elastomeric seal needs to be soft to accommodate installation but stiff to block fluid flow. Here we show that the two requirements are better fulfilled by a strain-stiffening elastomer than a neo-Hookean elastomer. We represent the strain-stiffening elastomer using the Gent model, and calculate the deformation in the elastomeric seal using an approach analogous to the lubrication theory of a viscous fluid between rigid walls. We determine the sealing pressure on the basis of two modes of leak. The seal leaks by elastic deformation when the fluid pressure exceeds the contact pressure between the seal and the rigid wall. The seal leaks by rupture when the energy release rate of a crack exceeds the toughness of the elastomer. For both modes of leak, a strain-stiffening elastomer enhances the sealing pressure compared to a neo-Hookean elastomer. We construct diagrams in which the two modes of leak are demarcated. It is hoped that this study will aid in the development of materials and geometries of seals.