  Nearly 50% of all sources detected by the Fermi Large Area Telescope are
classified as blazars or blazar candidates, one of the most elusive classes of
active galaxies. Additional blazars can also be hidden within the sample of
unidentified or unassociated $\gamma$-ray sources (UGSs) that constitute about
one-third of all gamma-ray sources detected to date. We recently confirmed that
the large majority of Fermi blazars of the BL Lac subclass have an X-ray
counterpart. Using the X-ray properties of a BL Lac training set and combining
these with archival multifrequency information, we aim to search for UGSs that
could have a BL Lac source within their $\gamma$-ray positional uncertainty
regions. We reduced and analyzed the Swift X-ray observations of a selected
sample of 327 UGSs. We then compared the X-ray fluxes and hardness ratios of
all sources detected in the pointed fields with those of known Fermi BL Lacs.
We find at least one X-ray source, lying within the $\gamma$-ray positional
uncertainty at 95% confidence level, for 223 UGSs and a total of 464 X-ray
sources in all fields analyzed. The X-ray properties of a large fraction of
them, eventually combined with radio, infrared, and optical information,
exhibit BL Lac multi-frequency behavior, thus allowing us to select
high-confidence BL Lac candidates; some of them were recently observed during
our optical spectroscopic campaign which confirmed their nature. We find that
out of 50 X-ray sources that were confirmed as BL Lacs through optical
spectroscopy, 12 do not show canonical mid-infrared or radio BL Lac properties.
This indicates that the selection of X-ray BL Lac candidates is a strong method
to find new counterparts within Fermi UGSs. Finally, we pinpoint a sample of 32
Swift/XRT candidate counterparts to Fermi UGSs that are most likely BL Lac
objects.
