Although drug development typically focuses on binding thermodynamics, recent studies suggest that kinetic properties can strongly impact a drug candidate's efficacy. Robust techniques for measuring inhibitor association and dissociation rates are therefore essential. To address this need, we have developed a pair of complementary isothermal titration calorimetry (ITC) techniques for measuring the kinetics of enzyme inhibition. The advantages of ITC over standard techniques include speed, generality, and versatility; ITC also measures the rate of catalysis directly, making it ideal for quantifying rapid, inhibitor-dependent changes in enzyme activity. We used our methods to study the reversible covalent and non-covalent inhibitors of prolyl oligopeptidase (POP). We extracted kinetics spanning three orders of magnitude, including those too rapid for standard methods, and measured sub-nM binding affinities below the typical ITC limit. These results shed light on the inhibition of POP and demonstrate the general utility of ITC-based enzyme inhibition kinetic measurements.