  Current and future B-mode polarization data are the most powerful observables
to constrain gravitational waves from the early Universe. We set conservative
constraints on tensor modes when relaxing the inflationary consistency
condition $n_t=-r/8$ between the tensor tilt $n_t$ and the tensor-to-scalar
ratio r. By adding a power-law spectrum of tensor perturbations to
$\Lambda$CDM, and parameterizing this tensor contribution by two independent
primordial tensor-to-scalar ratios $(r_1,r_2)$ at $k_1 = 0.005$ Mpc$^{-1}$ and
$k_2 = 0.02$ Mpc$^{-1}$, Planck and BICEP/Keck Array 2018 data (BK18) lead to
constraints $r_{0.005} < 0.030$ and $r_{0.02} < 0.098$ at 95% CL. The
corresponding upper bound $r_{0.01} < 0.039$ is by a factor of 2 tighter than
the one obtained with Planck 2018 and the older BK15 data. We then study the
perspectives for future CMB experiments that will measure both the reionization
bump and recombination peak of the B-mode polarization angular power spectrum,
such as LiteBIRD. We test the robustness of the results to the choice of the
scales for $(r_1,r_2)$ in these future perspectives. Whereas distinguishing
$n_t=-r/8$ from exact scale invariance is impossible as expected, we show how
radical, theoretically motivated departures from $n_t=-r/8$, which are
consistent with the current data, could be distinguished with LiteBIRD.
Moreover, LiteBIRD will be able to shrink the allowed parameter space area in
the $(r_{0.005},r_{0.02})$ plane to less than one hundredth of the currently
allowed area by Planck 2018 and BK18.
