  We analyzed low-background data from the CRESST-II experiment with a total
net exposure of 730 kg days to extract limits on double electron capture
processes. We established new limits for $^{40}$Ca with
$T_{1/2}^{2v2K}>9.9\times10^{21}$ y and $T_{1/2}^{0v2EC}>1.4\times10^{22}$ y
and for $^{180}$W with T$_{1/2}^{2v2K}>3.1\times10^{19}$ y and
$T_{1/2}^{0v2EC}>9.4\times10^{18}$ y at 90% CL. Depending on the process, these
values improve the currently best limits by a factor of $\sim$1.4-30.
