This paper presents wideband tunable band-stop filters working in the Ku to Ka-band frequencies based on a miniature single-MEM device combining a central capacitive MEM switch with AlN dielectric and inductive suspension arms. An outstanding 55% tuning range is achieved thanks to an original device design which features suspended-meander arm inductance with zipping capacitive coupling enabling a continuous tuning. Two band-stop filters have been designed for 13.5-29.5 GHz and 16-37 GHz frequency range resulting in rejection levels of -15 dB/-20 dB for the whole tuning range and band-pass insertion loss of -0.19 dB/-0.25 dB at 10 GHz, respectively. Temperature measurements have been performed from -100 degrees C to 100 degrees C demonstrating highly stable filter performances and tuning range, which recommends these devices for communications and airborne applications. For low temperatures (-100 degrees C), the pull-in voltage increases by 17% and the tuning range is slightly reduced. However, at same low temperature the filter rejection improves by more than 20% (up to -25 dB). An accurate circuit T-model has been proposed and validated against S-parameter measurements and 3D EM full wave simulations. The fabricated devices are very robust and show highly reproducible characteristics at wafer level; the filter characteristics in air and vacuum are quasi-identical, probably due to AlN dielectric slow charging/fast discharging. Moreover, filter characteristics stay stable over three month of wafer storage in ambient conditions.