The magnetic shape memory (MSM) effect occurs in some ferromagnetic martensitic alloys at temperatures below the martensite finish temperature and involves the re-orientation of martensite variants by twin boundary motion, in response to an applied stress and/or magnetic field. The driving force for twin boundary motion is the magnetic anisotropy. In this study, magnetization measurements as a function of magnetic field were made on several oriented single crystals of Ni-Mn-Ga alloys using a vibrating sample magnetometer. The magnetization versus magnetic field curves were characteristic of magnetically soft materials with magnetic anisotropy consistent with literature estimates for the different martensite structures observed in Ni-Mn-Ga alloys. Differences in the slope of the curves were due to the martensite structure, the relative proportion of martensite variants present, and their respective easy and hard axis orientations. Thermo-magneto-mechanical training was applied in an attempt to transform multi-variant specimens to single variant martensite. Training of the orthorhombic 7M martensites was sufficient to produce a near single variant of martensite, while the tetragonal 5M martensite responded well to training and produced a single-variant state. The strength of the uniaxial magnetic anisotropy constant for single-variant tetragonal 5M martensite, Ni52.9Mn27.3Ga19.8, was calculated to be Ku=1.8 x 105 J/m3, consistent with literature values. To obtain single-variant martensites, heat-treatment of the specimens prior to thermo-magneto-mechanical training is necessary.