  We present an investigation of the performance of the relativistic
multi-reference Fock-space coupled cluster (FSCC) method for predicting
molecular hyperfine structure (HFS) constants, including a thorough
computational study to estimate the associated uncertainties. In particular, we
considered the $^{19}$F HFS constant in the ground and excited states of BaF.
Due to a larger basis set dependence, the uncertainties on the excited state
results (16-85%) were found to be significantly larger than those on the ground
state constants ($\sim$2%). The ab initio values were compared to the recent
experimental results, and good overall agreement within the theoretical
uncertainties was found. This work demonstrates the predictive power of the
FSCC method and the reliability of the established uncertainty estimates, which
can be crucial in cases where the calculated property cannot be directly
compared to experiment.
