This paper reports for the first time on a novel concept of creating MEMS tuneable/switchable capacitors, by laterally moving of the sidewalls of a three-dimensional micromachined transmission line. Furthermore, the micro-electromechanical actuators are completely embedded inside the ground layer of the transmission line. The devices are based on a single-photolithography SOI RF MEMS process developed by the authors. Three different prototype designs have been fabricated and characterized, and model parameters were extracted which very well fit the measurement results. The min/max capacitive values are 43/76, 55/80, and 64/80 fF. The measured insertion loss for the best design are -0.3 dB without transmission line and -1.38 dB including the transmission line (20 GHz). The transmission lines alone were found to be more lossy than expected (1.1 dB/mm), which is attributed to difficulties in the control of the side-wall metallization thickness of this first prototype run.