This Letter demonstrates a measurement technique based on frequency-to-time mapping and coherent detection, which enables the complete (i.e., amplitude and phase) characterization of dynamically reconfigurable photonic filters. We apply this technique to a unit cell from a silicon CMOS-compatible photonic lattice filter that has a rapidly changing transfer function with an 8.33 ns update time, 120 MHz spectral resolution, and 12 GHz bandwidth. These dynamic measurements allow characterization of transients, thermal effects, filter fidelity, and other time-dependent phenomena during switching.