There is a growing demand for precision and high-quality optical objectives and lenses due to their numerous advantages and uses. The market for high precision objective lenses has tremendous potential for development and is a sector that is expanding quickly. Measuring the aberrations of optical systems is an essential step in the fabrication of high precision optical components. However, when working at the cutting-edge of technology, it is increasingly difficult to provide trustworthy measurements as the used metrology instrument has to be of comparable or higher precision. This poses a major problem especially when working with high numerical aperture (NA) optics. In this thesis, we will analyze and quantify the measurement uncertainty of a Twyman-Green interferometer used for lens testing of high-NA microscope objectives. To quantify the measurement uncertainty of the interferometer, various sources of uncertainty that affect the accuracy and precision of the measurements are considered. These include environmental and instrumentation factors such as incorrect phase-stepping, laser instability, camera noise, stray light, photon shot noise, effects of mid-spatial frequencies originating in the optical reference, as well as computational shortcomings such as: incorrect phase unwrapping, polynomial fit errors, incorrect pupil scaling and edge detection. By carefully analyzing these individual sources of uncertainty and their impact, we determine the overall measurement uncertainty of the interferometer and provide an assessment of its accuracy through Monte Carlo simulations, where the introduced uncertainties are obtained from real measurement data. The uncertainty analysis procedure described in this paper is a useful tool that can also be applied to different types of interferometers by taking proper considerations into account.