A method to determine material parameters by comparing the evolution of experimentally determined 3D microstructures to simulated 3D microstructures is proposed. The temporal evolution of a dendritic solid-liquid mixture is acquired in situ using x-ray tomography. Using a time step from these data as an initial condition in a phase-field simulation, the computed structure is compared to that measured experimentally at a later time. An optimization technique is used to find the material parameters that yield the best match of the simulated microstructure to the measured microstructure in a global manner. The proposed method is used to determine the liquid diffusion coefficient in an isothermal Al-Cu alloy. However, the method developed is broadly applicable to other experiments in which the evolution of the three-dimensional microstructure is determined in situ. We also discuss methods to describe the local variation of the best-fit parameters and the fidelity of the fitting. We find a liquid diffusion coefficient that is different from that measured using directional solidification.