It is expected on both evolutionary and empirical grounds that many merging neutron star (NS) binaries are composed of a highly magnetized NS in orbit with a relatively low magnetic field NS. I study the magnetic interactions of these binaries using the framework of a unipolar inductor model. The electromotive force generated across the non-magnetic NS as it moves through the magnetosphere sets up a circuit connecting the two stars. The exact features of this circuit depend on the uncertain resistance in the space between the stars R_(space). Nevertheless, I show that there are interesting observational and/or dynamical effects irrespective of its exact value. When R_(space) is large, electric dissipation as great as ~10^(46) erg s^(–1) (for magnetar-strength fields) occurs in the magnetosphere, which would exhibit itself as a hard X-ray precursor in the seconds leading up to merger. With less certainty, there may also be an associated radio transient. When R_(space) is small, electric dissipation largely occurs in the surface layers of the magnetic NS. This can reach ~10^(49) erg s^(–1) during the final ~1 s before merger, similar to the energetics and timescales of short gamma-ray bursts. In addition, for dipole fields greater than ≈10^(12) G and a small R_(space), magnetic torques spin up the magnetized NS. This drains angular momentum from the binary and accelerates the inspiral. A faster coalescence results in less orbits occurring before merger, which would impact matched-filtering gravitational-wave searches by ground-based laser interferometers and could create difficulties for studying alternative theories of gravity with compact inspirals
