  We compute the resummed on-shell $W^+ W^-$ production cross section under a
jet-veto at the LHC to partial N$^3$LL order matched to the fixed order NNLO
result. Differential NNLO cross sections are obtained from an implementation of
$q_T$ subtraction in Sherpa. The two-loop virtual corrections to the $q \bar q
\rightarrow W^+ W^-$ amplitude, used in both fixed order and resummation
predictions, are extracted from the public code {\tt qqvvamp}. We perform
resummation using soft collinear effective theory (SCET), with approximate beam
functions where only the logarithmic terms are included at two-loop. In
addition to scale uncertainties from the hard matching scale and the
factorization scale, rapidity scale variations are obtained within the analytic
regulator approach. Our resummation results show a decrease in the jet-veto
cross-section compared to NNLO fixed order predictions, with reduced scale
uncertainties compared to NNLL+NLO resummed predictions. We include the
loop-induced $gg$ contribution with jet veto resummation to NLL+LO. The
prediction shows good agreement with recent LHC measurements.
