Recently, weak measurements were used to measure small effects that are transverse to the propagation direction of a light beam. Here we address the question of whether weak measurements are also useful for measuring small longitudinal phase shifts. We show that standard interferometry greatly outperforms weak measurements in a scenario involving a purely real weak value. However, we also present an interferometric scheme based on a purely imaginary weak value, combined with a frequency-domain analysis, which may have the potential to outperform standard interferometry by several orders of magnitude.