Techniques for determining a damping rate of unforced oscillations of a meniscus are disclosed. An example method includes receiving input describing a shape of a container, physical parameters of a liquid inside the container, and an equilibrium shape of the meniscus. The method also includes generating a mesh conforming to the shape of the container and generating a discrete version of a continuous eigenvalue problem based on this mesh. The method also includes computing, at appropriate mesh nodes, values for pressure, velocity components, and meniscus surface deformation corresponding to a suitable number of least-damped late-time oscillation modes of the liquid and computing an angular frequency and damping rate of these least-damped late-time oscillation modes from the discrete version of the continuous eigenvalue problem. The method also includes identifying the mode that has the lowest damping rate and computing a liquid relaxation time by inverting the damping rate of the identified mode.