High Resolution Interference Microscopy (HRIM) is a technique that allows the characterization of amplitude and phase of electromagnetic wave-fields in the far-field with a spatial accuracy that corresponds to a few nanometers in the object plane. Emphasis is put on the precise determination of topological features in the wave-field, called phase singularities or vortices, which are spatial points within the electromagnetic wave at which the amplitude is zero and the phase is hence not determined. An experimental tool working in transmission with a resolution of 20 nm in the object plane is presented and its application to the optical characterization of various single and periodic nanostructures such as trenches, gratings, microlenses and computer generated holograms is discussed. The conditions for the appearance of phase singularities are theoretically and experimentally outlined and it is shown how dislocation pairs can be used to determine unknown parameters from an object. Their corresponding applications to metrology or in optical data storage systems are analyzed. In addition, rigorous diffraction theory is used in all cases to simulate the interaction of light with the nano-optical structures to provide theoretical confirmation of the experimental results.