We have measured the attenuation of picosecond electrical pulses by two-dimensional electron gases that are monolithically integrated in coplanar transmission lines. By integrating the two-dimensional electron gas structure into the transmission line, we avoid impedance mismatches that give rise to spurious reflection. The attenuated transients are simulated by an equivalent circuit transmission line model, where the conductivity of the two-dimensional electron gas underneath the transmission line is taken into account. The measured pulses are fitted with a specific conductivity of the layers corrected with a mode overlap factor, which describes the overlap of the electrical field lines with the two-dimensional layer. We obtain an overlap factor of 0.8–1.1.