In this paper, we explore an approach to actively plan and excite contact modes in differentiable simulators as a means to tighten the sim-to-real gap. We propose an optimal experimental design approach derived from information-theoretic methods to identify and search for information-rich contact modes through the use of contact-implicit optimization. We demonstrate our approach on a robot parameter estimation problem with unknown inertial and kinematic parameters which actively seeks contacts with a nearby surface. We show that our approach improves the identification of unknown parameter estimates over experimental runs by an estimate error reduction of at least $\sim 84\%$ when compared to a random sampling baseline, with significantly higher information gains.