In a reanalysis of the Vector Helium Magnetometer data taken by Pioneer 11 during its Saturn encounter in 1979, using improvements in the data set and in the procedures, studies are made of a variety of models. The best is the P1184 model, an axisymmetric spherical harmonic model of Saturn's magnetic field within 8 Saturn radii of the planet. Its coefficients for the internal sources are g1 0=0.2114, g2 0=0.0160, g3 0=0.0226 gauss and for the external sources G1 0=-7.1 nT while Pioneer 11 was approaching Saturn and -12.6 nT while it was leaving. The appropriately weighted root mean square average of the difference between the observed and the modeled field is 1.13%. For the Voyager-based Z3 model of Connerney, Acu¿a, and Ness, this average difference from the Pioneer 11 data is 1.81%. The external source currents in the magnetopause, tail, bow shock, and perhaps ring currents vary with time and can only be crudely modeled. An algebraic formula is derived for calculating the L shells on which energetic charge particles drift in axisymmetric fields.