The room-temperature crystal structures of undoped and doped barium and strontium cerate perovskite have been refined from medium-resolution, neutron time-of-flight powder diffraction data. The compounds BaCeO3, SrCeO3, BaCe0.85Pr0.15O3 and SrCe0.95Yb0.05O2.975 all crystallise in the orthorhombic space group Pmcn with the GdFeO3 structure type. The crystal structure of SrCeO3 was solved from high-resolution neutron powder data by determining the magnitudes of the octahedron tilt angles from the psuedocubic lattice constants, and then refining the two structural alternatives using the Rietveld method to determine the correct structure. The structures of both doped samples are only slightly different from those of the undoped ones, reflecting the good lattice match of these ions for Ce4+. The extrinsic anion vacancy could not be located unambiguously in SrCe0.95Yb0.05O2.975 and was found to be absent in BaCe0.85Pr0.15O3 in keeping with the expected stoichiometry. This contrasts with BaCe0.9Y0.1O2.95 where the vacancy was located on O-2.