We propose a low-cost and versatile method to measure flow rate in microfluidic channels under pressure-driven flows, thereby providing a simple characterization of the hydrodynamic permeability of the system. The technique is inspired by the current monitoring method usually employed to characterize electro-osmotic flows, and makes use of the measurement of the time-dependent electric resistance inside the channel associated with a moving salt front. We have successfully tested the method in a micrometer-size channel, as well as in a complex microfluidic channel with a varying cross-section, demonstrating its ability in detecting internal shape variations.