The properties of the interface between materials have practical implications in various fields, encompassing capillary action, foam and emulsion stability, adhesion properties of materials and mass and heat transfer processes. Studying the dynamics of interfaces is also fundamental for understanding intermolecular interactions, change of molecular conformations and molecular aggregations. Pendant-drop tensiometry and its extension, the oscillating drop method, are simple, versatile methods used to measure surface tension, interfacial tension and interfacial rheological properties. These methods can, however, generate unreliable results because of inadequate material preparation, an incorrect calibration method, inappropriate selection of data for analysis, neglect of optical influences or operating the system outside the linear viscoelastic regime. In addition, many studies fail to report accurate uncertainties. This protocol addresses all these critical points and provides detailed descriptions of some operation tips relating to purifying methods for different kinds of material, the time frame for analyzing measurement data, the correction method for optical effects, implementation of the oscillating method with a common programmable pump and remedies for some common problems encountered during the measurement. Examples of interfacial tension measurements for two- and three-phase systems, as well as interfacial dilational modulus measurements for N2 and surfactant solutions, are provided to illustrate procedural details and results. A single measurement takes minutes to hours to complete, while the entire protocol, including the leak test, cleaning, repeated measurements and data analysis, may take several days.