  We consider a nonlinear Neumann problem, with periodic oscillation in the
elliptic operator and on the boundary condition. Our focus is on problems posed
in half-spaces, but with general normal directions that may not be parallel to
the directions of periodicity. As the frequency of the oscillation grows,
quantitative homogenization results are derived. When the homogenized operator
is rotation-invariant, we prove the H\"{o}lder continuity of the homogenized
boundary data.
