We consider fixed-interval smoothing continuous-time partially observed Beneš systems and piecewise linear dynamical systems. Existing results for such smoothers require the use of two sided stochastic calculus. The main contribution of this paper is to present a robust formulation of the smoothing equations. Under this robust formulation, the smoothing equations are non-stochastic parabolic partial differential equations (with random coefficients) – and hence the technical machinery associated with two sided stochastic calculus is not required. Furthermore, the robust smoothed state estimates are locally Lipschitz in the observations – which is useful for numerical simulation.