We determine the linear viscoelastic properties of star polymer melts through an exact solution to the first-passage time expression developed by Milner and McLeish [Macromolecules 1997, 30, 2159] (MM), and compare with both the approximate solution proposed by MM and experimental data. The approximate and exact solutions show quite similar scalings of the terminal relaxation time with the number of entanglements per star arm n(e), with only a modest shift in time scale, accounting for the success of the approximate solution in treating moderately entangled stars. We also calculate the n(e), dependence of the recoverable shear compliance and the zero-shear viscosity and compare these with extensive data taken from the literature. Zero-shear viscosities for stars of four different monomer chemistries and a range of n(e) values are accurately represented by the MM theory, using plateau moduli and monomeric friction coefficients in good agreement with literature values.