We present a conceptual framework and the computational tools to study the value of the material responses in designing material characterization tests to identify the material model under uncertainty. A computational framework is first developed to estimate the information gained by observing a material response as a measure of the value of the experiment. The proposed framework is then extended to estimate the mutual information between the material response space and the material model space as a basis for ranking the available material response candidates as they relate to reducing the uncertainty of the inferred model. We then define a design problem where a tunable parameter, referred to as the design parameter, is identified so as to render two different material responses to be of the same value from an information content point of view. We finally study the value of the material responses, obtained in a spherical indentation test, i.e. reaction force–indenter displacement, maximum indentation load and the residual imprint, where it is shown that the proposed framework offers a computationally affordable and uncertainty-aware platform to design material characterization tests.