A search for exclusive or quasi-exclusive W+W- production by photon-photon interactions, pp -> p({*})W(+)W(-)p({*}), at \textbackslash{}/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 mu(+/-)mu(-/+) vertex with no additional associated charged tracks and dilepton transverse momentum p(T)(mu(+/-)mu(-/+)) > 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)/A(2) with a dipole form factor and an energy cutoff A(cutoff) = 500 GeV are of the order of 10(-4).