We present a method for the measurements of complex transmission coefficient through high transmission loss samples using three-sensors, two impedance tubes, monotonic wave excitation, and phase sensitive detection. Having demonstrated the effectiveness of the method on perforated plates measurements have been made on locally resonant sonic materials (LRSMs). The transmission losses of perforated plates are found to decrease with decreasing frequency down to 120Hz, following the mass law. For the LRSM’s panels with the same area mass density but different compositions, the local resonance frequency (at which the transmission loss is maximum) is found to vary according to the predesigned value. Transmission losses as high as 96.5dB at 630Hz and 87dB at 250Hz can be measured with good accuracy, with corresponding phase spectra that match the theoretical prediction of LRSMs, confirming the reliability of the transmission data.