  The search for neutrinos with energies greater than $10^{17}~$eV is being
actively pursued. Although normalization of the dominant neutrino flux is
highly uncertain, a floor level is guaranteed by the interactions of
extragalactic cosmic rays with Milky Way gas. We estimate that this floor level
gives an energy flux of $E^2\phi_\nu\simeq
10^{-13^{+0.5}_{-0.5}}~$GeV~cm$^{-2}$~sr$^{-1}$~s$^{-1}$ at $10^{18}~$eV, where
uncertainties arise from the modeling of the gas distribution and the
experimental determination of the mass composition of ultra-high-energy cosmic
rays on Earth. Based on a minimal model of cosmic-ray production to explain the
mass-discriminated energy spectra observed on Earth above
$5{\times}10^{18}$~eV, we also present generic estimates of the neutrino fluxes
expected from extragalactic production that generally exceed the aforementioned
guaranteed floor. The prospects for detecting neutrinos above $10^{18}$~eV
remain however challenging, unless proton acceleration to the highest energies
is at play in a sub-dominant population of cosmic-ray sources or new physical
phenomena are at work.
