It is common to determine the characteristic impedance <tex>${Z}_{0}$</tex> of a low-loss transmission line using the measured propagation constant <tex>$\gamma$</tex> through <tex>${Z}_{0}=\gamma/({G}+\mathrm{j}\omega {C})$</tex>, assuming that the parallel conductance <tex>${G}=0$</tex> and that the parallel capacitance <tex>$C$</tex> is constant. However, if the line is a coplanar waveguide or a microstrip, two dielectrics (substrate and air) are involved and its effective dielectric constant is frequency-dependent, which makes <tex>$C$</tex> also frequency-dependent. If so, the assumption <tex>$G=0$</tex> is inconsistent with causality constraints. This paper presents an attempt at determining <tex>${Z}_{0}$</tex> by augmenting the above method in a way consistent with causality. A method of calibration comparison with 2nd-tier multiline TRL is used to extract <tex>${Z}_{0,\text{meas}}$</tex> and <tex>$\gamma_{\text{meas}}$</tex>, following 1st-tier probe-tip calibration that is assumed to be valid at least up to 67 GHz. Then, a causal model, <tex>${Y}_{\mathrm{p},\mathrm{model}}$</tex>, of parallel admittance <tex>${G}(\omega)+\mathrm{j}\omega {C}(\omega)$</tex> is built from <tex>${Y}_{\mathrm{p}}^{\prime}=\gamma_{\text{meas}}/{Z}_{0,\text{meas}}\ (\underset{\sim}{<} \ 67$</tex> GHz) by network synthesis. <tex>${Y}_{\mathrm{p},\mathrm{model}}$</tex> and <tex>$\gamma_{\text{meas}}$</tex> are then used to determine <tex>${Z}_{0}$</tex> including <tex>$\underset{\sim}{>} 67$</tex> GHz. The method is applied to a CMOS transmission line from 20 MHz to 220 GHz. A well-built model gives well-behaved and plausible estimate of causal <tex>${Z}_{0}$</tex> over the entire measurement frequency range.