Electrocorticography (ECoG), electrophysiological recording from the pial surface of the brain, is a critical measurement technique for clinical neurophysiology, basic neurophysiology studies, and demonstrates great promise for the development of neural prosthetic devices for assistive applications and the treatment of neurological disorders. Recent advances in device engineering are poised to enable orders of magnitude increase in the resolution of ECoG without comprised measurement quality. This enhancement in cortical sensing enables the observation of neural dynamics from the cortical surface at the micrometer scale. While these technical capabilities may be enabling, the extent to which finer spatial scale recording enhances functionally relevant neural state inference is unclear. We examine this question by employing a high-density and low impedance 400 μm pitch microECoG (μECoG) grid to record neural activity from the human cortical surface during cognitive tasks. By applying machine learning techniques to classify task conditions from the envelope of high-frequency band (70-170Hz) neural activity collected from two study participants, we demonstrate that higher density grids can lead to more accurate binary task condition classification. When controlling for grid area and selecting task informative sub-regions of the complete grid, we observed a consistent increase in mean classification accuracy with higher grid density; in particular, 400 μm pitch grids outperforming spatially sub-sampled lower density grids up to 23%. We also introduce a modeling framework to provide intuition for how spatial properties of measurements affect the performance gap between high and low density grids. To our knowledge, this work is the first quantitative demonstration of human sub-millimeter pitch cortical surface recording yielding higher-fidelity state estimation relative to devices at the millimeter-scale, motivating the development and testing of μECoG for basic and clinical neurophysiology as well as towards the realization of high-performance neural prostheses.