A very low-loss tunable evanescent-mode cavity bandpass filter (BPF) with one-octave (6-12 GHz) tuning range is presented. To implement a very low-insertion loss with wideband operation, a new coaxial-feed structure is devised in the tunable BPF. Across the entire tuning range, the achieved insertion loss is less than 0.5 dB. The 3-dB fractional bandwidth varies from 6.1% at 6 GHz to 12% at 12 GHz. The tenability is realized using silicon microelectromechanical systems diaphragms with slits that are electrostatically actuated. Direct comparison between a solid diaphragm and the proposed stress-reduced diaphragm with slits is presented. The bulk of the filter is realized using physical machining of a tall printed circuit board. This article shows the upper frequency limit that is feasible using milling.