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This paper presents the modeling, design, fabrication, and measurement of microelectromechanical systems-enabled continuously tunable evanescent-mode electromagnetic cavity resonators and filters with very high unloaded quality factors (Qu). Integrated electrostatically actuated thin diaphragms are used, for the first time, for tuning the frequency of the resonators/filters. An example tunable resonator with 2.6:1 (5.0-1.9 GHz) tuning ratio and Qu of 300-650 is presented. A continuously tunable two-pole filter from 3.04 to 4.71 GHz with 0.7% bandwidth and insertion loss of 3.55-2.38 dB is also shown as a technology demonstrator. Mechanical stability measurements show that the tunable resonators/filters exhibit very low frequency drift (less than 0.5% for 3 h) under constant bias voltage. This paper significantly expands upon previously reported tunable resonators.