A re-scaling of a recent model of Jupiter's magnetosphere incorporating ring current, magnetopause, and tail current systems is used as a starting-point for modeling Saturn's magnetospheric field. The model is compared with observations obtained by Cassini during its Saturn orbit insertion fly-through of Saturn's magnetosphere, and is shown to give a good description. Comparison of ring current parameters obtained on the inbound and early outbound passes, when the magnetosphere was expanded due to low solar wind pressure, with those obtained by Voyager-1 under more usual conditions, and by Pioneer-11 when the magnetosphere was compressed, suggests that the ring current magnetic moment increases with system size. The effect is proposed to be due to radial stress balance conditions in a rapidly rotating magnetosphere, and has consequences for the dependence of magnetosphere size on solar wind pressure.