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We perform the first general relativistic force-free simulations of neutron star magnetospheres in orbit about spinning and nonspinning black holes. We find promising precursor electromagnetic emission: typical Poynting luminosities at, e.g., an orbital separation of r = 6.6/RNs are Lm ~ 6 X 1042(BNS,p/1013 G)²(MNS/1.4M⊙)² erg/s. The Poynting flux peaks within a broad beam of ~40° in the azimuthal direction and within ~60° from the orbital plane, establishing a possible lighthouse effect. Our calculations, though preliminary, preview more detailed simulations of these systems that we plan to perform in the future. [ABSTRACT FROM AUTHOR]