We present an original, easy to implement, reliable method of non-destructive testing of the orientation of carbon nanotubes by magnetic moment measurements performed in three perpendicular directions of magnetic field. Multi-wall carbon nanotubes/polystyrene composites were prepared by stretching and forge-rolling methods with the same nanotube loading. Unusually strong diamagnetic anisotropy in the composites prepared by the stretching method was observed and attributed to an additional diamagnetic response from the polystyrene aromatic rings wrapping the nanotubes. Strong anisotropy of diamagnetic susceptibility of the composites with highly aligned nanotubes correlates with anisotropic electromagnetic response and with improved microwave absorption properties. Both magnetic anisotropy and microwave absorbance is considerably lower in the composites prepared by the forge-rolled method. The magnetic results correlate well with polarized Raman spectroscopy. The research findings contribute to a better understanding of nanotube-polymer interface, alignment mechanisms, and ultimately the optimal design and performance of functional nanotube - aromatic polymer nanocomposites.