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Neutron stars in astrophysical binary systems represent exciting sources for multi-messenger astrophysics. A potential source of electromagnetic transients from compact binary systems is the neutron star ocean, the external fluid layer encasing a neutron star. We present a groundwork study into tidal waves in neutron star oceans and their consequences. Specifically, we investigate how oscillation modes in neutron star oceans can be tidally excited during compact binary inspirals and parabolic encounters. We find that neutron star oceans can sustain tidal waves with frequencies between $0.01-20$ Hz. Our results suggest that tidally resonant neutron star ocean waves may serve as a never-before studied source of precursor electromagnetic emission prior to neutron star-black hole and binary neutron star mergers. If accompanied by electromagnetic flares, tidally resonant neutron star ocean waves, whose energy budget can reach $10^{46}$ erg, may serve as early warning signs ($\gtrsim 1$ minute before merger) for compact binary mergers. Similarly, excited ocean tidal waves will coincide with neutron star parabolic encounters. Depending on the neutron star ocean model and a flare emission scenario, tidally resonant ocean flares may be detectable by Fermi and NuSTAR out to $\gtrsim 100$ Mpc with detection rates as high as $\sim 7$ yr$^{-1}$ for binary neutron stars and $\sim0.6$ yr$^{-1}$ for neutron star-black hole binaries. Observations of emission from neutron star ocean tidal waves along with gravitational waves will provide insight into the equation of state at the neutron star surface, the composition of neutron star oceans and crusts, and neutron star geophysics., 16 pages, 3 figures, 3 tables; accepted for publication in MNRAS