In this article we study the effects of a partial substitution of Ba with the smaller cation Ca in the layered cobaltites YBaCo2O 5+δ for δ ≈ 0.5. Neutron thermodiffractograms are reported for the compounds YBa0.95Ca0.05Co2O5.5 (xCa = 0.05) and YBa0.90Ca0.10Co2O5.5 (xCa = 0.10) in the temperature range 20 K ≤ T ≤ 300 K, as well as high resolution neutron diffraction experiments at selected temperatures for the samples xCa = 0.05, xCa = 0.10 and the parent compound xCa = 0. We have found the magnetic properties to be strongly affected by the cationic substitution. Although the "122" perovskite structure seems unaffected by Ca addition, the magnetic arrangements of Co ions are drastically modified: the antiferromagnetic (AFM) long-range order is destroyed, and a ferrimagnetic phase with spin state order is stabilized below T ∼ 290 K. For the sample with xCa = 0.05 a fraction of AFM phase coexists with the ferrimagnetic one below T ∼ 190 K, whereas for xCa = 0.10 the AFM order is completely lost. The systematic refinement of the whole series has allowed for a better understanding of the observed low-temperature diffraction patterns of the parent compound, YBaCo2O5.5, which had not yet been clarified. A two-phase scenario is proposed for the xCa = 0 compound which is compatible with the phase coexistence observed in the xCa = 0.05 sample.