  The ultrahigh energy range of neutrino physics (above $\sim 10^{7} \,
\mathrm{GeV}$), as yet devoid of detections, is an open landscape with
challenges to be met and discoveries to be made. Neutrino-nucleon cross
sections in that range - with center-of-momentum energies $\sqrt{s} \gtrsim 4
\, \mathrm{TeV}$ - are powerful probes of unexplored phenomena. We present a
simple and accurate model-independent framework to evaluate how well these
cross sections can be measured for an unknown flux and generic detectors. We
also demonstrate how to characterize and compare detector sensitivity. We show
that cross sections can be measured to $\simeq ^{+65}_{-30}$% precision over
$\sqrt{s} \simeq$ 4-140 TeV ($E_\nu = 10^7$-$10^{10}$ GeV) with modest energy
and angular resolution and $\simeq 10$ events per energy decade. Many allowed
novel-physics models (extra dimensions, leptoquarks, etc.) produce much larger
effects. In the distant future, with $\simeq 100$ events at the highest
energies, the precision would be $\simeq 15\%$, probing even QCD saturation
effects.
