Tunable resonant absorption by plasmons in the two-dimensional electron gas (2DEG) of grating-gated HEMTs is known for a variety of semiconductor systems, giving promise of chip-scale frequency-agile THz imaging spectrometers. In this work, we present our approach to measurement of electrical response to millimeter waves from backward-wave oscillators (BWO) in the range 40-110 GHz for InP-based HEMTs. Frequency-modulation of the BWO with lock-in amplification of the source-drain current gives an output proportional to the change in absorption with frequency without contribution from non-resonant response. This is a first step in optimizing such devices for manportable or space-based spectral-sensing applications.