A waveguide switch design using electromagnetic bandgap (EBG) substrates as the 3cm-long covers for the top and bottom surfaces of a standard Ku-band Waveguide have been investigated. The gap size in the front side metal pattern determines the EBG resonant frequency at which the large surface impedance prevents $TE_10$ mode from propagating in the waveguide. A simple modification to the EBG cover design can improve the switch frequency bandwidth performance. Experiments showed that varying the gap size in the EBG, thus changing the resonant frequency at different locations, produces an increase of 200 percent in the switch rejection bandwidth of better than 20 dB. The complete waveguide switch can be built by loading switching devices, such as RF MEMS switches or diodes, on the EBG to instantaneously convert the large surface impedance to regular metal impedance. Efforts are currently being made to fabricate monolithic MEMS-switchable EBG substrates for millimeter-wave applications.