Superhydrophobic surfaces have potential for reducing hydrodynamic drag by combining a structured surface and hydrophobicity to retain a lubricating air layer (plastron) at the surface. In the present contribution, numerical simulations of laminar flow past a superhydrophobic sphere are conducted using a two-phase flow representation. The results show drag reductions in Stokes flow of up to 19% for an air-water system, in agreement with previous analytic work, and demonstrate an increased effect as the Reynolds number is increased to 100. Drag reductions of up to 50% are achieved due to reduction in viscous drag and suppression of separation by the plastron, resulting in a narrower wake. To explore a less idealised model of the plastron, baffles have also been introduced to simulate the support of a plastron by roughness elements. The baffles lead to the attached vortex regime no longer being suppressed, but separation is delayed and drag reductions are evident in comparison to a solid sphere. Increasing the area solid fraction results in a diminished drag reduction due to the plastron, however drag reductions of up to 15% can still be achieved with solid fractions of 10%.