We have proposed for the first time, a novel way to generate coherent x-rays and γ-rays by using the process of 'stimulated electromagnetic shock radiation' (SESR). By adjusting the values of the parameters of the three agents (an electron beam, an electromagnetic wave (laser) and a dielectric medium) responsible for producing SESR, it may be possible to get the desired SESR output in terms of, both, its frequency and intensity. By studying the variation of SESR with respect to the external parameters in their feasible ranges we have selected those combinations of the parameters that give outputs close to the existing schemes to generate coherent x-rays. We have considered such different cases of interest and calculated numerical values of the output frequency, and the output power, by using the results of our classical second order relativistic calculations (Risbud A A 2004 J. Phys. A: Math. Gen. 37 6837; Risbud A A and Kamerkar N C 2001 Phys. Rev. E 63 036501). We have shown that the use of SESR may provide a new, cost-effective way to generate coherent, tunable x-rays and γ-rays by reducing, on the input side, the power requirements on both, the electron beam and the laser, while increasing the emitted frequency and power on the output side.