We have developed a dielectric measurement system for recovering the properties of bulk tissue samples utilizing a specialized configuration of our microwave tomographic imaging system. We exploit the fact that the sample's location, shape and size can be determined a priori based on the known fixture geometry and integrate this with a soft prior algorithm to essentially recover a single dielectric property within the target zone. This is potentially an important approach for cases where the widely applied coaxial probe approach is not optimal due to poor surface contact and property differences between the surface and tissue interior. For example, the treated surface of a sample of cancellous bone can be quite heterogeneous given the intricate web of trabeculae, fat and marrow. Our technique is able to reconstruct a value for this sample which is indicative of the whole volume.