In this paper, we apply the theory of fundamental design limitations to haptic interface systems that employ only motion sensors. A multivariable feedback controller connects a haptic device with a virtual environment, where the design objective is accurate rendering of the force/motion response of the environment to the operator. We consider the control design without force sensing and extend previous work by determining fundamental limits on the achievable performance. We also apply a tradeoff between performance and stability robustness, inherent to certain multivariable systems, to show that the best achievable performance induces compromised stability robustness. A controller that attains the limiting performance is compared against a standard spring-damper virtual coupler with a simulation study.