A bstract We present a phenomenology study on central exclusive production of W + W − boson pairs in proton-proton collisions at the Large Hadron Collider at 14 TeV using the forward proton detectors, such as the ATLAS Forward Proton or the CMS-TOTEM Precision Proton Spectrometer detectors. Final states where at least one of the W bosons decay hadronically in a large-radius jet are considered. The latter extends previous efforts that consider solely leptonic final states. A measurement of exclusive W + W − also allows us to further constrain anomalous quartic gauge boson interactions between photons and W bosons. Expected limits on anomalous quartic gauge couplings a 0 , C W associated to dimension-six effective operators are derived for the hadronic, semi-leptonic, and leptonic final states. It is found that the couplings can be probed down to one-dimensional values of a 0 W = 3.7 × 10 − 7 GeV − 2 and a C W = 9.2 × 10 − 7 GeV − 7 at 95% CL at an integrated luminosity of 300 fb − 1 by combining all final states, compared to values of about a 0 W = 4 × 10 − 6 GeV − 2 and a C W = 1 × 10 − 5 GeV − 2 at 95% CL expected for the leptonic channel alone.