  Perturbative calculations of gradient flow observables are technically
challenging. Current results are limited to a few quantities and, in general,
to low perturbative orders. Numerical stochastic perturbation theory is a
potentially powerful tool that may be applied in this context. Precise results
using these techniques, however, require control over both statistical and
systematic uncertainties. In this contribution, we discuss some recent
algorithmic developments that lead to a substantial reduction of the cost of
the computations. The matching of the ${\overline{\rm MS}}$ coupling with the
gradient flow coupling in a finite box with Schr\"odinger functional boundary
conditions is considered for illustration.
