Problems of high-power microwaves penetrating into and reflecting from a semiconductor (silicon) plate with non-stationary processes are investigated. The plate is the basis of switches activated by laser-driven photoconductivity which changes its properties when heated by the switched microwave power. Analytical criteria for the stationary solutions of the activated (quasi-metallic) and deactivated (dielectric) states of the switch under the conditions of high-power microwave heating and external cooling are found. Results of numerical simulations are also given for the problems of the switch activation by microwave heating initiated by pulsed laser radiation, which increases the carrier density rapidly. Numerical simulations are carried out using the finite-difference time-domain method with the unsplit perfectly matched layer absorbing boundary conditions. We demonstrate various types of solutions depending on the basic parameters of the problems - microwave field intensity, laser pulse energy and semiconductor doping.