The pressure gradient across stenotic blood vessels is an important clinical index for the diagnosis of many cardiovascular diseases. While clinical gold standard for its measurement (in terms of accuracy) is invasive catheterization, Phase-Contrast MR-imaging has emerged as a promising tool for enabling a non-invasive quantification, by linking (highly spatially resolved) velocity measurements with relative pressures via Navier-Stokes equations. In this work we provide a review of current methods for relative pressure estimation, propose new ones and compare them on numerical examples using subsampled and noisy synthetic data. We verify that the newly proposed approaches are more robust with respect to data perturbations and therefore more precise.