[en] Parametric x-ray or quasi-Cherenkov radiation is produced by the passage of an electron through a crystal. A critical absorber technique has been employed to investigate its linewidth. Experiments have been performed with the 855MeV electron beam from the Mainz Microtron MAMI. Thin absorber foils were mounted in front of a CCD camera serving as a position sensitive photon detector. Upper limits of the linewidth of 1.2 and 3.5eV were determined for the (111) and (022) reflections of silicon at photon energies of 4966 and 8332eV. These limits originate from geometrical line broadening effects that can be optimized to reach the ultimate limit given by the finite length of the wave train. copyright 1997 The American Physical Society