A search for exclusive or quasi-exclusive W+W− production by photon-photon interactions, pp → p(*)W+W−p(*), at 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 aW0,C/Λ2 with a dipole form factor and an energy cutoff Λcutoff = 500 GeV are of the order of 10−4.