  We observed four nearby spiral galaxies (NGC 3627, NGC 4254, NGC 4736 and NGC
5055) in the K band with the 64-m Sardinia Radio Telescope, with the aim of
detecting the Anomalous Microwave Emission (AME), a radiation component
presumably due to spinning dust grains, observed so far in the Milky Way and in
a handful of other galaxies only (most notably, M 31). We mapped the galaxies
at 18.6 and 24.6 GHz and studied their global photometry together with other
radio-continuum data from the literature, in order to find AME as emission in
excess of the synchrotron and thermal components. We only find upper limits for
AME. These non-detections, and other upper limits in the literature, are
nevertheless consistent with the average AME emissivity from the few
detections: it is $\epsilon^\mathrm{AME}_{\mathrm{30~GHz}} = 2.4\pm0.4 \times
10^{-2}$ MJy sr$^{-1}$ (M$_\odot$ pc$^{-2}$)$^{-1}$ in units of dust surface
density (equivalently, $1.4\pm0.2 \times 10^{-18}$ Jy sr$^{-1}$ (H
cm$^{-2}$)$^{-1}$ in units of H column density). We finally suggest to search
for AME in quiescent spirals with relatively low radio luminosity, such as
M~31.
