A model for the magnetic field strength along a stellarator field line has been developed which correctly describes the principal contributions to the field strength and which can differ substantially from the simple form commonly assumed. An analytically tractable form of the model is obtained and is compared with results from ray-tracing in real fields. A theoretical description of the drift motions of 'localized' particles (trapped in the helical ripples of the magnetic field) is then obtained for a more general class of stellarator field than previously possible. Orbits in real devices are considered for both ℓ = 2 and ℓ = 3, and differences between the predictions of the present work and of earlier investigations are pointed out. The application of the theory to particle guiding-centre orbit following is discussed, and other consequences of the improved model field are indicated.