Microwave approaches to breast imaging include the measurement of signals transmitted through and reflected from the breast. Prototype systems typically feature sensors separated from the breast, resulting in measurements that include the effects of the environment and system. To gain insight into transmission of microwave signals through the breast, a system that places sensors in direct contact with the breast is proposed. The system also includes a lossy immersion medium that enables measurement of the signal passing through the breast while significantly attenuating signals traveling along other paths. Collecting measurements at different separations between sensors also provides the opportunity to estimate the average electrical properties of the breast tissues. After validation through simulations and measurements, a study of 10 volunteers was performed. Results indicate symmetry between the right and left breast and demonstrate differences in attenuation, maximum frequency for reliable measurement, and average properties that likely relate to variations in breast composition.