We compute the magnetic shielding tensor within the London approximation and estimate the Knight shift of single-wall carbon nanotubes. Our results indicate that high resolution 13C NMR should be able to separate the metallic and insulator character of the nanotubes since a 11 ppm splitting is predicted from the respective resonances. As a model for disorder, bending, and defects in these structures, we investigate the magnetic response of nanotubes with finite size. We get a small line broadening coming from an intrinsic length dependent resonance effect. The nanotube packing is also studied and leads to a 20 ppm broadening which disappears under experimental high-resolution conditions.