You would have to run the experiment in reverse, that is, apply a known magnetic field, measure the Zeeman splitting Δf and from there calculate h by Δf=2*γ*B, with γ=g_e*μ_B/h, where g_e = 2.003 is the NV electronic Landé factor, μ_B the Bohr magneton and h is Planck’s constant.
Easier though to run an experiment like this to derive Planck's constant:
-branadic-