Recent advances in MR technology have enabled increased spatial resolution for routine functional and anatomical imaging, which has created demand for software tools that are able to process these data. The availability of high-resolution data also raises the question of whether higher resolution leads to substantial gains in accuracy of quantitative morphometric neuroimaging procedures, in particular the cortical surface reconstruction and cortical thickness estimation. In this study we adapted the FreeSurfer cortical surface reconstruction pipeline to process structural data at native submillimeter resolution. We then quantified the differences in surface placement between meshes generated from (0.75 mm)3 isotropic resolution data acquired in 39 volunteers and the same data downsampled to the conventional 1 mm3 voxel size. We find that when processed at native resolution, cortex is estimated to be thinner in most areas, but thicker around the Cingulate and the Calcarine sulci as well as in the posterior bank of the Central sulcus. Thickness differences are driven by two kinds of effects. First, the gray–white surface is found closer to the white matter, especially in cortical areas with high myelin content, and thus low contrast, such as the Calcarine and the Central sulci, causing local increases in thickness estimates. Second, the gray–CSF surface is placed more interiorly, especially in the deep sulci, contributing to local decreases in thickness estimates. We suggest that both effects are due to reduced partial volume effects at higher spatial resolution. Submillimeter voxel sizes can therefore provide improved accuracy for measuring cortical thickness.