Studies of biochemical liquids require precise determination of their complex permittivity. We developed a microwave characterization technique on the basis of a high-quality whispering-gallery mode (WGM) sapphire resonator with a microfluidic channel filled with the liquid under test. A novel approach allows obtaining the complex permittivity of biochemical liquids of sub-microliter/nanoliter volumes with high accuracy. The method is based on a special procedure of analysis of the interaction of electromagnetic field with liquid in a WGM microfluidic resonator and measurements of both the WGM resonance frequency shift and the change of the inverse quality factor. The approach is successfully applied to obtain the complex permittivity in the Ka-band of glucose, albumin bovine serum, lactalbumin, and cytochrome C aqueous solutions using the developed microwave technique.