We present medium-resolution observations of nine QSOs whose lines-of-sight pass within 45 h-1 kpc of low-redshift (Z(gal) < 0.2) galaxies. We fail to detect Ca II absorption at the galaxies' redshift down to 2-sigma equivalent-width limits of between 38 and 164 m-angstrom in all but one quasar spectrum, 1543 + 489. With these data, supplemented by previously published results, we attempt to establish the Ca II absorption cross-sections of present-day galaxies by defining an unbiased sample of QSO-galaxy pairs for which all observations have been reported, regardless of the success or otherwise of the search for absorption. With the exception of the very weak lines seen in the spectrum of 1543 + 489, we find that Ca II absorption - when observed - is strong (W-lambda greater-than-or-similar-to 350 m-angstrom) and occurs within approximately 11 h-1 kpc or 2.3 Holmberg radii from the centre of the galaxy. There exist, however, several examples of QSO-galaxy pairs with separations less than this which do not show absorption. By considering the six systems in which absorption is already known, we conclude that Ca II is confined either to galaxy discs, or distributed inhomogeneously around a galaxy, at least at the equivalent-width limits currently detectable. We conclude that there is no evidence for spherical, calcium-absorbing haloes with unity covering factor around present-day galaxies. We briefly contrast these conclusions with the observations of Mg II haloes at intermediate redshifts. In the case of 1543 + 489, we observe K and H absorption at a redshift of 0.075, with equivalent widths of 62 +/- 22 and 82 +/- 22 m-angstrom, respectively. These are the weakest Ca II lines from an external galaxy yet detected in a quasar spectrum. They appear to be due to a bright, anonymous galaxy 45 h-1 kpc from the quasar sight-line, the largest separation of all QSO-galaxy pairs known to show Ca II absorption. We speculate, however, that the absorber may actually be a dwarf galaxy only 6 h-1 kpc away from the line-of-sight.