In the present paper an approach to reduce uncertainty in the measurement of the dielectric constant of a rectangular dielectric slab situated in a rectangular waveguide is discussed. The experimental model under consideration consists of two rectangular full height and full width slabs located in an otherwise empty section of a rectangular waveguide. The dielectric constant of one of these slabs is to be measured, while the dielectric constant of the other slab is known (measured with high accuracy in advance). The slab with known constitutive properties is introduced for the purpose of altering the shape of the curve representing the relationship between the absolute value of the reflection coefficient and the dielectric constant to be measured, since curves having larger steepness in the neighborhood of the actual value of the dielectric constant result in smaller values of uncertainty. Although it is possible to change the shape of the curve by varying sample parameters, an increase in steepness obtained this way is not always sufficient. Furthermore, it is not always possible or convenient to alter dimensions of the sample under test and/or frequency. The results of the present study show that this issue can be overcome by extending the experimental model, i.e., by introducing an auxiliary dielectric slab with known constitutive properties. Additionally, it is shown that under certain conditions it is always possible to increase the steepness of the curve in the range of values in which the value of the dielectric constant is expected to fall, by varying the thickness of the auxiliary slab and distance between the slabs. The efficiency of the proposed approach is confirmed by results of numerical modeling.