The problem of nonprehensile robotic catching is addressed using virtual nonholonomic constraints (VNHCs); the motion of the robot end-effector is designed and controlled directly in terms of the states of the object before it is caught on the surface of the end-effector. In contrast to contemporary approaches, our approach avoids the need for object trajectory prediction, and consequent time-varying robot trajectory generation. With a focus on the planar case, we demonstrate that our VNHC approach can be used to catch an object on an end-effector at a desired height, with minimal relative normal velocity at the contact instant. Moreover, the VNHC function depends only on the desired catching height, and the same VNHC can be used for a range of initial conditions. We use model predictive control (MPC) to bring the object and end-effector to rest at a desired location after contact is made. The approach is validated in simulation.