In the present paper, the high-sensitivity technique for reducing the uncertainty of the free-space measurements of the real part of the permittivity of dielectric slab is proposed. The real part of the permittivity is extracted from the absolute value of the reflection coefficient measured by means of horn antenna. It is shown that making measurements for the slab under test (SUT) alone (original experimental model), in many cases results in large uncertainty because of low sensitivity of the model in the range of possible values of the real part of permittivity. The total measurement uncertainty depends on the slope of the measurement curve that can be used as a measure of the sensitivity of the model; consequently, to reduce it one has to increase the slope of the measurement curve that can be achieved by varying parameters of the model, such as the operating frequency or thickness of SUT. However, when the measurements are to be made in a non-destructive manner at a given frequency (in case of highly dispersive materials), neither frequency, nor thickness can be changed thus making it impossible to increase the slope of the measurement curve in the region of interest and, therefore, reduce the uncertainty. To overcome the problem we propose to extend the original model by introducing into it one or two auxiliary slabs (extended model) with known constitutive properties thereby extending the set of model parameters affecting the shape of the curve. Alternatively, with extended models one can achieve higher sensitivity without having to vary the frequency and thickness. Optimal choice of dimensions of auxiliary slab(s) is discussed in detail herein. The validity of the proposed method is verified through numerical experiments.