Here, we proposed two delay lines consisting of spoof Surface Plasmon Polariton (sSPP) waveguides and C-shaped metamaterials (C-MMs). The delay lines, namely OFF and ON devices, were designed and fabricated. On the OFF device, an sSPP waveguide is capacitively coupled to the C-MMs via an air gap on a high-resistivity silicon substrate. On the ON device, a connection is established between the C-MMs and the sSPP waveguide by metal connectors. The difference in the electrical properties in the coupling between the C-MMs and the sSPP waveguide creates a large phase contrast between the ON and OFF delay lines. The structural design was performed using a numerical calculation based on a commercial finite element solver. We successfully fabricated and characterized delay lines with phase differences equal to tens of degrees between the ON and OFF devices in the target frequency range of 2-6 GHz, while maintaining the original transmittance properties. The promising applications of the delay lines are a phase shifter or modulator when integrating with suitable switches.