Effective and efficient retrieval of similar shapes from large image databases is still a challenging problem in spite of the high relevance that shape information can have in describing image contents. We propose a novel Fourier-based approach, called WARP, for matching and retrieving similar shapes. The unique characteristics of WARP are the exploitation of the phase of Fourier coefficients and the use of the dynamic time warping (DTW) distance to compare shape descriptors. While phase information provides a more accurate description of object boundaries than using only the amplitude of Fourier coefficients, the DTW distance permits us to accurately match images even in the presence of (limited) phase shillings. In terms of classical precision/recall measures, we experimentally demonstrate that WARP can gain, say, up to 35 percent in precision at a 20 percent recall level with respect to Fourier-based techniques that use neither phase nor DTW distance.