An inverted micro-strip line (IML) is proposed at microwave and millimeter wave frequencies. This IML on high resistivity silicon (HRS) is studied from 10 to 100 GHz and presents an attenuation lower than 0.08 dB/mm on the whole frequency band. A parametric study, in order to minimize the attenuation and the dispersion of the inverted line in the 10-100 GHz bandwidth, is performed using numerical full wave calculations with HFSS (High Frequency Structural Simulator) tool. A complementary study is added: a large variety of characteristic impedances (for instance, from 38 Ω to 87 Ω at 60 GHz) is performed, the change of propagation modes is observed and the qualification and quantification of the losses allows minimizing them. A comparison with a line of the same length and width without ground plane, the Planar Goubau Line (PGL) is reported in the 10-100 GHz band and a first measure of the PGL is performed, in the 55-67 GHz band, presenting the same propagation mode as the IML at 60 GHz. The measured attenuation of 0.064 dB/mm in the 55-67 GHz obtained for the PGL promises a comparable value for the IML in the measured band.