Monolithic methods are often accurate but not always feasible due to time-scale or solver requirement differences between the subsystems, redesigning costs, inaccessibility to some subsystem internal information, etc. Co-simulation is an alternative to monolithic methods which can involve simultaneous simulation of multiple interconnected physical systems using different simulation tools. Model-based coupling relies on a reduced model of the mechanical subsystem. During the macro time step, the interfacing subsystems, mechanical or other domain, interact with this model only. This study presents two approaches for model-based co-simulation of non-smooth systems which extends our previous work focused on model order reduction of the smooth systems. A reduced interface model is developed by transforming the generalized velocities of the mechanical system to the subset of interface velocities. In co-simulation, it is generally assumed that the reduced model will only be valid for a short time interval where corresponds to the macro time step. As a first step in developing the reduced model, we determine which unilateral contacts are active at the beginning of the selected time interval. Once the active set is known, one approach is to assume that all contacts in the mechanical system are always active, i.e., bilateral, and that the system can be modelled with a smooth model. This results in a smooth-RIM formulation. In non-smooth systems, smooth-RIM may not accurately represent a non-smooth system if new contact states are formed during the macro step. To address this problem, we propose to include potential contacts that are prone to open or close into the formulations. These potential contacts are maintained in complementarity form, and the smooth reduced model is augmented with them to result in a non-smooth reduced model in the form of a complementarity problem. The study used a 7-degree-of-freedom spatial robotic manipulator to test the performance of the proposed reduced interface models in a co-simulation setup. Smooth-RIMs have shown promising results in multiple non-smooth model simulations. However, the obtained results in this study show that the smooth-RIM formulation cannot always give a correct reduced model of a non-smooth system and can be limiting in certain cases.