Context. Departures from local thermodynamic equilibrium (LTE) distort the calcium abundance derived from stellar spectra in various ways, depending on the lines used and the stellar atmospheric parameters. The collection of atomic data adopted in non-LTE (NLTE) calculations must be sufficiently complete and accurate. Aims: We derive NLTE abundances from high-quality observations and reliable stellar parameters using a model atom built afresh for this work, and check the consistency of our results over a wide wavelength range with transitions of atomic and singly ionised calcium. Methods: We built and tested Ca I and Ca II model atoms with state-of-the-art radiative and collisional data, and tested their performance deriving the Ca abundance in three benchmark stars: Procyon, the Sun, and Arcturus. We have excellent-quality observations and accurate stellar parameters for these stars. Two methods to derive the LTE/NLTE abundances were used and compared. The LTE/NLTE centre-to-limb variation (CLV) of Ca lines in the Sun was also investigated. Results: The two methods used give similar results in all three stars. Several discrepancies found in LTE do not appear in our NLTE results; in particular the agreement between abundances in the visual and infra-red (IR) and the Ca I and Ca II ionisation balance is improved overall, although substantial line-to-line scatter remains. The CLV of the calcium lines around 6165 Å can be partially reproduced. We suspect differences between our modelling and CLV results are due to inhomogeneities in the atmosphere that require 3D modelling.