We derive a generally applicable formula to calculate the precision of multi-parameter measurements that apply least squares algorithms. This formula, which accounts for experimental noise and uncertainty in the controlled model parameters, is then used to analyze the uncertainty of thermal property measurements with pump-probe thermoreflectance techniques. We compare the uncertainty of time domain thermoreflectance and frequency domain thermoreflectance (FDTR) when measuring bulk materials and thin films, considering simultaneous measurements of various combinations of thermal properties, including thermal conductivity, heat capacity, and thermal boundary conductance. We validate the uncertainty analysis using Monte Carlo simulations on data from FDTR measurements of an 80 nm gold film on fused silica.