However, correct description of interactions between charged water-soluble molecules and membranes has been challenging for atomistic resolution models employed in molecular dynamics (MD) simulations. Canonical force fields tend to overestimate the binding affinities of sodium and calcium to membranes, yet this can be improved by electronic continuum correction (ECC) or additional repulsive potential (NBFIX). Also lipid-protein interactions depend on force field parameters, particularly for charged residues and their interactions with lipid headgroups. Furthermore, charged residues in strongly membrane-bound peptides appear as potential sources of discrepancies in comparisons with NMR data and often lead to the largest deviations from experimental hydrophobicity scales. These findings raise the question of whether the interactions between charged molecules and membranes can be correctly captured in MD simulations without including electronic polarizability or other corrections. Therefore, it is currently not clear how accurately atomistic MD simulations can predict interactions between membranes and charged molecules, such as drugs, amino acids, or pollutants. Sodium and calcium ion binding affinities to membranes with various compositions have been quantitatively evaluated in simulations using the changes in lipid headgroup C-H bond order parameters, which depend on the accumulation of charges on the membrane. Here we apply the same approach to quantify the binding affinities of etidocaine and tetraphenylphosphonium (TPP) ions to a POPC lipid bilayer, serving as a model cellular membrane. Etidocaine is a clinically used local anaesthetic and serves here as a model for charged drug binding to a membrane. TPP is a hydrophobic ion historicaly used to establish the concept of membrane dipole potential and serves as a model for charged aromatic compounds which are common among potentially bioaccumulant ions. Our results compare the relative binding affinities of these molecules to membranes with respect to sodium and calcium and test the quality of MD simulations regarding these affinities. Furthermore, we also investigate the binding mechanisms of these small molecules to membranes and the effect of implicit inclusion of electronic polarizability using ECC.