In heavy flavour physics, the D- and B-meson sectors continue to be promising realms for precision tests of the Standard Model,where evidence of New Physics can be expected. Lattice QCD offers a powerful ab initio framework to reliably calculate the low-energy hadronic amplitudes, which are crucial for the determination of CKM matrix elements, and thus to significantly reduce the uncertainties of the theory inputs to such tests. This talk presents results on the leptonic D-meson decay constants obtained from a large number of (2+1)-flavour ensembles with O(a) improved Wilson quarks by CLS (including two ensembles at the physical point), spanning 6 lattice spacings down to 0.039 fm and lying on 3 trajectories in the quark mass plane. This allows achieving a phenomenologically relevant precision, while demonstrating control over important sources of systematic uncertainties such as discretisation effects and the quark mass dependence. The second part discusses a strategy how to combine interpolations between relativistic and static computations with a step scaling approach, in order to extract heavy-light B-physics observables in the continuum. We report first numerical results for the b-quark mass and leptonic decay constants from a subset of CLS ensembles and outline how this strategy also applies to semi-leptonic form factors.