Phase correlation (PC) is widely employed by several sub-pixel motion estimation techniques in an attempt to accurately and robustly detect the displacement between two images. To achieve sub-pixel accuracy, these techniques employ interpolation methods and function-fitting approaches on the cross-correlation function derived from the PC core. However, such motion estimation techniques still present a lower bound of accuracy that cannot be overcome. To allow room for further improvements, we propose in this paper the enhancement of the sub-pixel accuracy of motion estimation techniques by employing a completely different approach: the concept of motion magnification. To this end, we propose the novel phase amplified correlation (PAC) that integrates motion magnification between two compared images inside the phase correlation part of frequencybased motion estimation algorithms and thus directly substitutes the PC core. The experimentation on magnetic resonance (MR) images and real video sequences demonstrates the ability of the proposed PAC core to make subtle motions highly distinguishable and improve the sub-pixel accuracy of frequency-based motion estimation techniques.