Experimental assessment or prediction of plant steady state is important for many applications in the area of modeling and operation of continuous processes. For example, the iterative implementation of static real-time optimization requires reaching steady state for each successive operating point, which may be quite time-consuming. This paper presents an approach to speed up the estimation of plant steady state for imperfectly known dynamic systems that are characterized by (i) the presence of fast and slow states, with no effect of the slow states on the fast states, and (ii) the fact that the unknown part of the dynamics depends only on the fast states. The proposed approach takes advantage of measurement-based rate estimation, which consists in estimating rate signals without the knowledge or identification of rate models. Since one can use feedback control to speed up the convergence to steady state of the fast part of the plant, this rate estimation allows estimating the steady state of the slow part during transient operation. It is shown how this approach can be used to speed up the static real-time optimization of continuous processes. A simulated example illustrates its application to a continuous stirred-tank reactor.