Rapid and selective molecular exchange across a barrier is essential for emulating the properties of biological membranes. Vertically-aligned carbon nanofibre (VACNF) forests have shown great promise as membrane mimics, owing to their mechanical stability, their ease of integration with microfabrication technologies and the ability to tailor their morphology and surface properties. However, quantifying transport through synthetic membranes having micro- and nanoscale features is challenging. Here, fluorescence recovery after photobleaching (FRAP) is coupled with finite difference and Monte Carlo simulations to quantify diffusive transport in microfluidic structures containing VACNF forests. Anomalous subdiffusion was observed for FITC (hydrodynamic radius of 0.54 nm) diffusion through both VACNFs and SiO(2)-coated VACNFS (oxVACNFs). Anomalous subdiffusion can be attributed to multiple FITC-nanofibre interactions for the case of diffusion through the VACNF forest. Volume crowding was identified as the cause of anomalous subdiffusion in the oxVACNF forest. In both cases the diffusion mode changes to a time-independent, Fickian mode of transport that can be defined by a crossover length (R(CR)). By identifying the space-and time-dependent transport characteristics of the VACNF forest, the dimensional features of membranes can be tailored to achieve predictable molecular exchange.