The mesonic $f_{PS} / m_V$ and $f_V / m_V$ ratios, with $f$ the decay constant and $m$ the meson mass, are calculated in mass perturbed conformal gauge theories to NNLO and N^3LO orders, respectively. Here NNLO and N^3LO refer to the non-relativistic effective theory expansion which is the applicable framework. The results are expanded a la Banks-Zaks in order to end up with scheme-independent predictions. These perturbative results are unambiguously reliable close to the upper end of the conformal window, $N_f$ = 16.5 and it is shown that they might be reliable down to $N_f$ = 12. An attempt is made to match these to previous non-perturbative lattice results in the range $1 < N_f < 11$. An abrupt change in the ratios is observed at around $N_f = 12 - 13$, which may signal the lower end of the conformal window.