Accurate predictions of hyperfine structure (HFS) constants are important in many areas of chemistry and physics, from the determination of nuclear electric and magnetic moments to benchmarking of new theoretical methods. We present a detailed investigation of the performance of the relativistic coupled cluster method for calculating HFS constants within the finite-field scheme. The two selected test systems are Cs-133 and (BaF)-Ba-137. Special attention has been paid to construct a theoretical uncertainty estimate based on investigations on basis set, electron correlation and relativistic effects. The largest contribution to the uncertainty estimate comes from higher order correlation contributions. Our conservative uncertainty estimate for the calculated HFS constants is similar to 5.5%, while the actual deviation of our results from experimental values is <1% in all cases.