  Jet vetoes play an important role in many analyses at the LHC. Traditionally,
jet vetoes have been imposed using a restriction on the transverse momentum
$p_{Tj}$ of jets. Alternatively, one can also consider jet observables for
which $p_{Tj}$ is weighted by a smooth function of the jet rapidity $y_j$ that
vanishes as $|y_j| \to \infty$. Such observables are useful as they provide a
natural way to impose a tight veto on central jets but a looser one at forward
rapidities. We consider two such rapidity-dependent jet veto observables,
$\mathcal{T}_{Bj}$ and $\mathcal{T}_{Cj}$, and compute the required beam and
dijet soft functions for the jet-vetoed color-singlet production cross section
at two loops. At this order, clustering effects from the jet algorithm become
important. The dominant contributions are computed fully analytically while
corrections that are subleading in the limit of small jet radii are expressed
in terms of finite numerical integrals. Our results enable the full NNLL'
resummation and are an important step towards N3LL resummation for cross
sections with a $\mathcal{T}_{Bj}$ or $\mathcal{T}_{Cj}$ jet veto.
