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A two-pole evanescent-mode waveguide narrow-band filter digitally tunable with micro-electromechanical system (MEMS) switches is demonstrated. A design approach for a prescribed frequency shift and tuning range is elaborated using a simple equivalent circuit model. The validity of the proposed frequency tuning concept is proved through simulation and measurement of a prototype. The measured tunable filter achieves three resonant states around 3 GHz, with an average frequency tuning of 20 MHz between each state, a fractional 1-dB bandwidth of 1.2-1.5% and better than 2.1 dB insertion loss. The measured unloaded quality factor (Q) of the filter varies from 315 to 460 over the frequency tuning range.