Abstract: Pair production of W gauge bosons is an important process at the LHC entering many experimental analyses, both as background in new-physics searches or Higgs measurements and as signal in precision studies and tests of the Standard Model. Therefore, accurate predictions for this class of processes are of great interest in order to exploit the full potential of LHC measurements. We use the LoopSim method to combine NLO QCD results for WW and WW + jet, as well as the loop-squared gluon-fusion contribution, to obtain approximate NNLO predictions for WW production. The cross sections are calculated with VBFNLO and include leptonic decays of the W bosons as well as finite-width and off-shell effects. We find that the size of the additional corrections beyond NLO can be significant and well outside of the NLO error bands given by renormalization and factorization scale variation. Applying a jet veto, we observe further negative corrections at NNLO. which we relate to the presence of large Sudakov logarithms.