This work presents the development of a noninvasive technique of investigating biological tissues, which is based on the method of resonant near field microwave tomography. Being new in medical practice, this method allows one to determine subsurface distributions of dielectric permittivity and conductivity of a medium by using the results of measuring the impedance of small antennas which are located on the medium surface and included in resonant sensors. As a probing element, we use the edge capacity of a cylindrical condenser with external coating and a metal flange end. Such a configuration of the near-field antenna makes it possible to minimize the negative influence of the pressing and measurements data distortions caused by the pressure of the sensor on the biological tissue. We work out a theoretical approach to finding the dependences of impedance characteristics of the near-field antennas, which contact the surface of a medium characterized by an inhomogeneous profile of the complex permittivity, and present examples of solving the inverse problem for subsurface probing in the case of layered media.