Stretchable electrical interconnects based on serpentines combined with elastic materials are utilized in various classes of wearable electronics. However, such interconnects are primarily for direct current or low-frequency signals and incompatible with microwave electronics that enable wireless communication. In this paper, design and fabrication procedures are described for stretchable transmission line capable of delivering microwave signals. The stretchable transmission line has twisted-pair design integrated into thin-film serpentine microstructure to minimize electromagnetic interference, such that the line's performance is minimally affected by the environment in close proximity, allowing its use in thin-film bioelectronics, such as the epidermal electronic system. Detailed analysis, simulations, and experimental results show that the stretchable transmission line has negligible changes in performance when stretched and is operable on skin through suppressed radiated emission achieved with the twisted-pair geometry. Furthermore, stretchable microwave low-pass filter and band-stop filter are demonstrated using the twisted-pair structure to show the feasibility of the transmission lines as stretchable passive components. These concepts form the basic elements used in the design of stretchable microwave components, circuits, and subsystems performing important radio frequency functionalities, which can apply to many types of stretchable bioelectronics for radio transmitters and receivers.