The effect of random signal lines on the on-chip inductance is quantitatively investigated, using an S-parameter-based methodology and a full wave solver, leading to an empirical model for high-frequency inductance. The results clearly indicate that the random signal lines as well as designated ground lines provide return paths for gigahertz-frequency signals. In particular, quasi TEM-wave-like propagation mode is observed above 10 GHz, revealing a unique relationship between capacitance and inductance of the signal line. Incorporating the random capacitive coupling effect, our frequency-dependent RLC model is confirmed to be valid up to 100 GHz.