This paper examines the quantification of uncertainty in weather derivatives pricing. The focus is on the propagation of a posterior distribution on uncertain model parameters through to relevant payoff statistics, summarizing the uncertainty using variance based credible intervals for any given payoff statistic. We also demonstrate the use of sensitivity analysis to determine the most influential parameters on the credible interval size. This paper serves a multitude of purposes. Firstly, we provide a basic review of the underlying theory behind uncertainty/sensitivity analysis, along with authors' novel ideas for numerical implementation. We also provide a novel and informative set of numerical results for credible interval computation and sensitivity analysis for a market relevant 5-station temperature problem. This paper serves as a foundation for exploring the use of Bayesian uncertainty/sensitivity quantification in weather derivatives portfolio management.