Microelectromechanical system (MEMS) varactors based on a freestanding layer of single-walled carbon nanotube (SWCNT) films were designed, fabricated and tested. The freestanding SWCNT film was employed as a movable upper patch in the parallel plate capacitor of the MEMS. The measurements of the SWCNT varactors show very high tunability, nearly 100%, of the capacitance with a low actuation voltage of 10 V. The functionality of the varactor is improved by implementing a flexible nanocellulose aerogel filling.