The Advanced LIGO observatories detected gravitational waves from two binary black hole mergersduring their first observation run (O1). We present a high-energy neutrino follow-up search for the secondgravitational wave event, GW151226, as well as for gravitational wave candidate LVT151012.We find twoand four neutrino candidates detected by IceCube, and one and zero detected by ANTARES, within +-500 saround the respective gravitational wave signals, consistent with the expected background rate. None ofthese neutrino candidates are found to be directionally coincident with GW151226 or LVT151012.We usenondetection to constrain isotropic-equivalent high-energy neutrino emission from GW151226, adoptingthe GW event’s 3D localization, to less than 2 × 1051–2 × 10^54 erg.