A major challenge in the discovery of the new antibiotics against Gram-negative bacteria is to achieve sufficiently fast permeation in order to avoid high doses causing toxic side effects. So far, suitable assays for quantifying the uptake of charged antibiotics into bacteria are lacking. We apply an electrophysiological zero-current assay using concentration gradients of β-lactamase inhibitors combined with single-channel conductance to quantify their flux rates through OmpF. Molecular dynamic simulations provide in addition details on the interactions between the nanopore wall and the charged solutes. In particular, the interaction barrier for three β-lactamase inhibitors is surprisingly as low as 3-5 kcal/mol and only slightly above the diffusion barrier of ions such as chloride. Within our macroscopic constant field model, we determine that at a zero-membrane potential a concentration gradient of 10 μM of avibactam, sulbactam, or tazobactam can create flux rates of roughly 620 molecules/s per OmpF trimer.