By employing redox-active probes, condensed-phase molecular transport through nanoporous thin films can often be measured electrochemically. Certain kinds of electrode materials (e.g. conductive glass) are difficult to fabricate as rotatable disks or as ultramicroelectrodes - the configurations most often used for electrochemical permeation measurements. These limitations point to the need for a more materials-general measurement method. Herein, we report the application of walljet electrochemistry to the study of molecular transport through model metallopolymeric films on indium tin oxide electrodes. A quantitative expression is presented that describes the transport-limited current at the walljet electrode in terms of mass transport through solution and permeation through the film phase. A comparison of the film permeabilities for a series of redox probes measured using the walljet electrode and a rotating disk electrode establishes the accuracy of the walljet method, while also demonstrating similar precision for the two methods. We apply this technique to a system consisting of zirconium phosphonate assembled films of a porphyrinic molecular square. Transport through films comprising three or more layers is free from significant contributions from pinhole defects. Surprisingly, transport through films of this kind is 2-3 orders of magnitude slower than through films constructed via interfacial polymerization of nearly identical supramolecular square building blocks (Keefe; et al. Adv. Mater. 2003, 15, 1936). The zirconium phosphate assembled films show good size exclusion behavior. The details of the observed dependence of permeation rates on probe molecule size can be rationalized with a model that assumes that the walls of the squares are slightly tilted from a strictly vertical geometry, consistent with atomic force microscopy measurements, and assumes that the individual wall geometries are locked by rigid interlayer linkages.