A bstract A search for exclusive or quasi-exclusive W + W − production by photon-photon interactions, pp → p (*) W + W − p (*) , at $ \sqrt{s}=7 $ TeV is reported using data collected by the CMS detector with an integrated luminosity of 5.05 fb −1 . Events are selected by requiring a μ ± e ∓ vertex with no additional associated charged tracks and dilepton transverse momentum p T ( μ ± e ∓ ) > 30 GeV. Two events passing all selection requirements are observed in the data, compared to a standard model expectation of 2.2 ± 0.4 signal events with 0.84 ± 0.15 background. The tail of the dilepton p T distribution is studied for deviations from the standard model. No events are observed with p T > 100 GeV. Model-independent upper limits are computed and compared to predictions involving anomalous quartic gauge couplings. The limits on the parameters $ {{{a_{0,C}^W}} \left/ {{{\varLambda^2}}} \right.} $ with a dipole form factor and an energy cutoff Λ cutoff = 500 GeV are of the order of 10 −4 .