An analyte permeation testing instrument with an edge leakage minimizing feature and a method of measuring permeability of a test film for a target analyte utilizing the analyte permeation testing instrument. The instrument includes a cartridge and a target analyte sensor. The cartridge has separable first and second plates having first and second cells respectively. The plates are operable for engaging a test film therebetween so as to sealingly separate the first and second cells. A surround around at least one of the first cell and the second cell projects within the interface between the first and second plates for engaging a periphery of the test film to compress the test film and thereby form a peripheral edge seal when the plates are clamped together.