Probability distributions for the location of the Saturnian bow shock and magnetopause have been derived by extrapolating observations of dynamic solar wind pressures to the position of Saturn's orbit. These observations are those made by the Pioneer 11, Voyager 1 and 2 spacecraft near Saturn's orbit and by the Ulysses spacecraft near its aphelion. The magnetopause subsolar distance (measured from Saturn's center) is obtained using pressure equilibrium. The bow shock standoff distance is determined using empirical relations between bow shock size and solar wind dynamic pressure. Simple 2-D geometric models of the magnetopause and bow shock surfaces have been used to determine their morphologies over a large range in local time. Three cases have been studied: (1) An Earth-type magnetosphere with low internal plasma pressure; (2) An intermediate case calibrated with Voyager 1 observations; and (3) A Jupiter-like inflated magnetosphere. The comparison of these models with initial observations from the initial sunward orbits of the Cassini spacecraft indicates a more inflated magnetosphere than postulated by the previous modelling of the Pioneer-Voyager encounters.