Room temperature experimental compression test data is available for different hardmetals. This data indicates the presence of some spatial inhomogeneity due to a compression instability, eccentric loading or time varying equivalent bending moment. To account for this, an inverse analysis is employed that determines not only the constitutive material model parameter values but also the displacement boundary conditions that best replicate the experimental data. The unknown boundary displacement history is approached using a systematically refined piecewise linear approximation, determined alongside material parameter values. The systematic simultaneous estimation of material parameter values and boundary approximations is also investigated using a virtual problem for which the exact solution is known. This investigation confirms that known material parameter values and boundary conditions can be recovered without using any prior knowledge of the exact displacement boundary conditions.