Monte Carlo simulations may be used to efficiently estimate critical properties of complex evolving systems but are nevertheless computationally intensive. Hence, when only part of a system is new or modified it seems wasteful to re-simulate the parts that have not changed. It also seems unnecessary to perform many simulations of parts of a system whose behaviour does not vary significantly. To increase the efficiency of designing and testing complex evolving systems we present simulation techniques to allow such a system to be verified against behaviourpreserving statistical abstractions of its environment. We propose a frequency domain metric to judge the a priori performance of an abstraction and provide an a posteriori indicator to aid construction of abstractions optimised for critical properties.