A new approach is proposed based on the use of electrodes modified with carbon nanomaterials to determine enzymatic activity and screening for inhibitors of serine β-lactamases such as extended spectrum β-lactamases (ESBLs). These enzymes are responsible for the development of antibiotic resistance of pathogenic bacteria to β-lactam antibiotics. Electrochemical oxidation of cephalosporin antibiotic cefotaxime was effectively registered at a potential E from +596 to +625 mV (relative to Ag/AgCl). This property makes it possible to determine the change in cefotaxime concentration in solution upon interaction with serine β-lactamases. By analyzing the electrochemical characteristics of the cefotaxime oxidation reaction, the kinetic parameters of its hydrolysis catalyzed by the serine β-lactamase CTX-M-116 were determined. The Michaelis constant was KM = 50 µM and the maximum rate of the catalytic reaction was 1.67∙10–6 M/min. A comparative analysis of the electrochemical parameters of the enzyme/substrate cefotaxime and enzyme/substrate cefotaxime/inhibitor sulbactam (SBT) systems was carried out. Inhibition of β-lactamase by sulbactam was characterized by an IC50 value of 2.5 μM. The proposed approach can be used for screening new substrates and inhibitors of β-lactamases.