Numerical simulation is used widely in the marine renewable energy sector. Wave and flow models are used to understand and predict the conditions experienced at offshore energy sites. Like all numerical simulations, wave models have uncertainties in their output caused by uncertainty about the various input data (which may themselves be model outputs), and uncertainty about how well the model simulates the real world. Understanding these uncertainties is important in order to hold confidence in the models accuracy. Classical Monte Carlo uncertainty analysis requires a large number of model runs which is impossible in large complex models if the computational run time is more than a few seconds. By substituting a much more computationally efficient mathematical model, known as an emulator, for the complex simulation then processing time can be decreased to a level where uncertainty analysis can be undertaken. A simple ’toy’ wave model has been produced using SWAN. By using a Bayesian methodology on output from a small number of correctly designed model runs, a mathematical emulator is constructed to provide a statistical approximation of output from the model. Importantly this emulator provides not just an approximation of the output but a full probability distribution describing how close the emulator output is to the model. As this emulator provides results in a fraction of a second (compared to several seconds for the toy simulator and considerably longer for actual wave models) it can be run many thousands of times as is required for a Monte Carlo analysis. This paper describes the methodology used to construct an emulator of a simulation and provides method and results using the emulator to undertake uncertainty quantification. The methods described here can be scaled up and employed on large wave models, flow models or any deterministic numerical simulator.