Abstract The search for neutrinos with energies greater than 1017 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 ϕ ν ≃ 10 − 13 − 0.5 + 0.5 GeV cm − 2 sr − 1 s − 1 at 1018 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 × 1018 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 1018 eV remain challenging, however, unless proton acceleration to the highest energies is at play in a subdominant population of cosmic-ray sources or new physical phenomena are at work.