There are several advantages to the use of band-stop filters, rather than band-pass filters, in many systems. This is shown to be particularly true when signals at high-power levels must be transmitted or rejected. A formula has been derived which expresses the external Q of each resonator in a band-stop filter in terms of the element values of the normalized low-pass prototype and the parameters of the frequency transformation. The peak power capacity of iris-coupled waveguide cavity filters and TEM filters using capacitively coupled inductive stubs is then determined in terms of the external Q of the first resonator and the dimensions of the resonator. Experimental results given for a waveguide band-stop filter show good agreement with theory.