Superflow of 3He–B in a channel can be observed by nuclear magnetic resonance (nmr) techniques, the simplest arrangement being one in which the magnetic field is perpendicular to the flow. Above a certain critical velocity, the transverse resonance frequency shifts away from the Larmor frequency, and the velocity gives a value of the ratio of the flow coupling constant to the dipole coupling constant, which is found to differ substantially from theoretical prediction. The nmr shifts can be used to detect persistent currents in a doubly connected geometry, and some preliminary observations are described as well as an analysis of the way in which currents with multiply quantized circulation may be set up.