High-aspect-ratio, porous membrane of vertically-aligned carbon nanotubes (CNTs) were developed through a templated microfabrication approach for electrochemical sensing. Nanostructured platinum (Pt) catalyst was deposited onto the CNTs with a facile, electroless deposition method, resulting in a Pt-nanowire-coated, CNT sensor (PN-CNT). Convection mass transfer enhancement was shown to improve PN-CNT sensor performance in the non-enzymatic, amperometric sensing of hydrogen peroxide (H2O2). In particular, convective enhancement was achieved through the use of high surface area to fluid volume structures and concentration boundary layer confinement in a channel. Stir speed and sensor orientation especially influenced the measured current in stirred environments for sensors with through-channel diameters of 16 µm. Through-flow sensing produced drastically higher signals than stirred sensing with over 90% of the H2O2 being oxidized as it passed through the PN-CNT sensor, even for low concentrations in the range of 50 nM to 500 µM. This effective utilization of the analyte in detection demonstrates the utility of exploiting convection in electrochemical sensing. For through-flow at 100 µL s-1, a sensitivity of 24,300 µA mM-1 cm-2 was achieved based on the frontal projected area (871 µA mM-1 cm-2 based on the nominal microchannel surface area), with a 0.03 µM limit of detection and a linear sensing range of 0.03-500 µM.