Engineered enzymes with enhanced or novel functions are specific catalysts with wide-ranging applications in industry and medicine. Here, we introduce Droplet Array Microfluidic Enzyme Kinetics (DA-MEK), a high-throughput enzyme screening platform that combines water-in-air droplet microarrays formed on patterned superhydrophilic/omniphobic surfaces with cell-free protein synthesis to enable cost-effective expression and quantitative kinetic characterization of enzyme variants. By printing DNA templates encoding enzyme variants onto hydrophilic spots, stamping slides to add cell-free expression mix, and imaging the resulting arrays, we demonstrate reproducible expression of hundreds of enzyme variants per slide. Subsequent stamping of fluorogenic substrates and time-lapse imaging allows determination of Michaelis-Menten parameters for each variant, with measured catalytic efficiencies spanning 5 orders of magnitude and agreeing well with values obtained via traditional microtiter plate assays. DA-MEK consumes orders of magnitude less reagents than plate-based assays while providing accurate and detailed kinetic information for both beneficial and deleterious mutations. In future work, we anticipate DA-MEK will provide a powerful and versatile platform to accelerate enzyme engineering and enable screening of large variant libraries under diverse conditions.