We have made {it XMM-Newton/} observations of 14 Galactic Cepheids that have candidate resolved ($geq$5$arcsec$) companion stars based on our earlier {it HST/} WFC3 imaging survey. Main-sequence stars that are young enough to be physical companions of Cepheids are expected to be strong X-ray producers in contrast to field stars. {it XMM-Newton/} exposures were set to detect essentially all companions hotter than spectral type M0 (corresponding to 0.5 $ M_odot$.) The large majority of our candidate companions were not detected in X-rays, and hence are not confirmed as young companions. One resolved candidate (S~Nor #4) was unambiguously detected, but the Cepheid is a member of a populous cluster. For this reason, it is likely that S~Nor #4 is a cluster member rather than a gravitationally bound companion. Two further Cepheids (S~Mus and R~Cru) have X-ray emission that might be produced by either the Cepheid or the candidate resolved companion. A subsequent {it Chandra} observation of S Mus shows that the X-rays are at the location of the Cepheid/spectroscopic binary. R Cru and also V659 Cen (also X-ray bright) have possible companions closer than 5$arcsec$ (the limit for this study) which are the likely source of X-rays. One final X-ray detection (V473 Lyr) has no known optical companion, so the prime suspect is the Cepheid itself. It is a unique Cepheid with a variable amplitude.
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