This paper presents possibilities of an error reduction of the phase estimation with an interpolated discrete Fourier transform (DFT). The properties of interpolations are studied for the rectangular and Harming windows with respect to their ability for correction systematic effects. The correction is improved by considering the leakage effect of the component spectrum. Uncertainties of the phase estimations have been studied. The simulation and experimental results are presented, showing the effectiveness in estimating the phase of the signal component.