Uncertainty quantification is essential in qualifying materials for use in a fusion reactor as constraining the uncertainty on crystal plasticity model parameters provides improved confidence intervals on the probability of component failure. The copper alloy CuCrZr will be used to construct the coolant pipes in future reactors and power plants. Although extensive work has been done in the preliminary qualification of CuCrZr, there are currently no experimental facilities that can replicate the mechanical, thermal, and electromagnetic loads expected in an operational fusion reactor. This work focusses on calibrating parameters in phenomenological crystal plasticity models using data from CuCrZr experimental tests to begin evaluating the microstructural response under well-characterised experimental conditions. Initially, data from simple experiments, such as tensile tests, were used to assess the limitations of the model and identify necessary refinements. Statistical variations in the microstructure have been used to run multiple simulations, creating a distribution of material input parameters. A Markov chain Monte Carlo method was then implemented to propagate the initial uncertainties and provide confidence intervals in the simulation outputs, such as the variance in microstructure surface-averaged stress-strain curves. The results from this research will be used in future work to compare phenomenological crystal plasticity models to dislocation density-based models for CuCrZr microstructure simulations. Alternative uncertainty quantification methods will be implemented with the aim of maintaining accuracy while reducing computation time.