We present a novel frequency-domain motion estimation technique, which operates on hexagonal images and employs the hexagonal Fourier transform. Our method involves image sampling on a hexagonal lattice followed by a normalised hexagonal cross-correlation in the frequency domain. The term subpixel (or subcell) is defined on a hexagonal grid in order to achieve floating point registration. Experiments using both artificially induced motion and actual motion demonstrate that the proposed method outperforms the state-of-the-art in frequency-domain motion estimation operating on a square lattice, in the shape of phase correlation, in terms of subpixel accuracy for a range of test material and motion scenarios.