Under the joint action of homogeneous magnetic fields and ambient media, relativistic charged particles emit synchrotron‐Cˇerenkov radiation. The behavior of this radiation in the vicinity of an atomic absorption edge is studied in detail. Theoretical estimates indicate that synchrotron‐Cˇerenkov radiation can be exploited for the measurement of dispersive interactions in the x‐ray region of the spectrum in parameter ranges not accessible by other techniques. TheKedge of krypton appears to be a conceptually clean‐cut case which is particularly suited for experimental tests; detailed predictions for the intensity of synchrotron‐Cˇerenkov radiation in the vicinity of thisKedge are given. With 20‐GeV electrons and fields of the order of a few kilogauss, it should be possible to measure deviations from unity of the index of refraction to a precision of 1 part in 109at photon energies of 14.3 keV.