Understanding of the liquid imbibition dynamics in nanoporous materials is important to advances in chemical separations, phase change heat transfer, electrochemical energy storage, and diagnostic assays. We study the liquid imbibition behavior in films of ceramic-coated vertically aligned carbon nanotubes (CNTs). The nanoscale porosity of the films is tuned by conformal ceramic coating via atomic layer deposition (ALD), enabling stable liquid imbibition and precise measurement of the imbibition dynamics without capillary densification of the CNTs. We show that the imbibition rate decreases as the ceramic coating thickness increases, which effectively changes the CNT-CNT spacing and therefore decreases the permeability. We derive a model, based on Darcy's law, that incorporates an expression for the permeability of nanoscale post arrays, and we show that the model fits the experimental results with high accuracy. The tailorable porosity, along with controllable surface wettability and mechanical stability of coated CNTs, suggest their suitability for application-guided engineering, and for further investigation of imbibition behavior at finer length scales.