The passive permeability of cell membranes is of key importance in biology, biomedical research and biotechnology as it determines the extent to which various molecules such as drugs, products of metabolism, and toxins can enter or leave the cell unaided by dedicated transport proteins. The quantification of passive solute permeation is possible with radio-isotope distribution experiments, spectroscopic measurements and molecular dynamics simulations. This protocol describes stopped-flow fluorimetry measurements performed on lipid vesicles and living yeast cells to estimate the osmotic permeability of water and solutes across (bio)membranes. Encapsulation of the fluorescent dye calcein into lipid vesicles allows monitoring of volume changes upon osmotic shifts of the medium via (de)quenching of the fluorophore, which we interpret using a well-defined physical model that takes the dynamics of the vesicles into account to calculate the permeability coefficients of solutes. We also present analogous procedures to probe weak acid and base permeability in vesicles and cells by using the read-out of encapsulated or expressed pH-sensitive probes. We describe the preparation of synthetic vesicles of varying lipid composition and determination of vesicle size distribution by dynamic light scattering. Data on membrane permeation are obtained using either conventional or stopped-flow kinetic fluorescence measurements on instruments available in most research institutes and are analyzed with a suite of user-friendly MATLAB scripts ( https://doi.org/10.5281/zenodo.6511116 ). Collectively, these procedures provide a comprehensive toolbox for determining membrane permeability coefficients in a variety of experimental systems, and typically take 2-3 d.