We report on the response of microchannel plates (MCPs) to single relativistic particles and to electromagnetic showers. Particle detection by means of secondary emission of electrons at the MCP surface has long been proposed and is used extensively in ion time-of-flight mass spectrometers. What has not been investigated in depth is their use to detect the ionizing component of showers. The time resolution of MCPs exceeds anything that has been previously used in calorimeters and, if exploited effectively, could aid in the event reconstruction at high luminosity colliders. Several prototypes of photodetectors with the amplification stage based on MCPs were exposed to cosmic rays and to 491 MeV electrons at the INFN-LNF Beam-Test Facility. The time resolution and the efficiency of the MCPs are measured as a function of the particle multiplicity, and the results used to model the response to high-energy showers.