Modeling contact can be quite tricky.
A key thing to remember is that the solver does not know the shape of a body in SimMechanics; it only knows the locations of the various coordinate systems (CG, CS1, CS2.... CS#). Without knowledge of the shape of the body surfaces, it cannot directly model contact between them. Note that if you brought in the model from SolidWorks using SimMechanics Link, the cool looking pieces in the visualization are graphical, it only uses what you can see in the block diagram for the actual simulation.
The general method for contact modeling involves detecting the distance between two bodies and applying a force to each of them. This requires adding sensors to the bodies, performing calculations on the sensed values, and using actuators to apply the forces and torques.
A simple version of this, mech_bouncing_ball.mdl, is found in the SimMechanics demos. This shows unidirectional contact force (from plane to ball). This model is simplified by the fact that the ball is symmetric, the plane is stationary, and no reaction force is exerted on the plane.
In addition to normal forces, you would also need to model friction between the ball and gripper so that it does not just fall out. This can also be calculated in a similar fashion as above, or using techniques described here.