Abstract: Monte Carlo sampling under equality constraints is relevant in many applications. In the study of molecular dynamics, in particular, it is often needed to sample the so-called conditional probability measure on the level set of a reaction coordinate function. In this talk, I will introduce a consistent Monte Carlo scheme that samples the conditional probability measure for a given reaction coordinate. I will present the analysis of error estimates concerning the long time sampling efficiency. Its applications in simulating the coarse-grained dynamics will also be discussed.