Bacterial biofilms are a metabolically heterogeneous community of bacteria distributed in an extracellular matrix comprised primarily of hydrated polysaccharides. Effective inhibitory concentrations measured under planktonic conditions are not applicable to biofilms, and inhibition concentrations measured for biofilms vary widely. Here, we introduce a novel microfluidic approach for screening respiration inhibition of bacteria in a biofilm array morphology. The device geometry and operating conditions allow antimicrobial concentration and flux to vary systematically and predictably with space and time. One experiment can screen biofilm respiratory responses to many different antimicrobial concentrations and dosing rates in parallel. To validate the assay, onset of respiration inhibition following NaN₃ exposure is determined optically using an O₂-sensing thin film. Onset of respiration inhibition obeys a clear and reproducible pattern based on time for diffusive transport of the respiration inhibitor to each biofilm in the array. This approach can be used for high-throughput screening of antimicrobial effectiveness as a function of microbial characteristics, antimicrobial properties, or antimicrobial dosing rates. The approach may also be useful in better understanding acquired antimicrobial resistance or for screening antimicrobial combinations.