A number of methods for estimating the translational friction coefficient f and the intrinsic viscosity [eta] of polymers and nanoparticles have been proposed. These methods range from first-principles "boundary-element" or "bead-model" solutions of the Stokes equation employing a precise description of particle shape, to coarse-grained descriptions of polymer structures and approximate computational methods at an intermediate level of description, and finally to phenomenological estimates that relate f to the surface area of the particle. Analytic treatments normally involve slender-body and various "preaveraging" approximations, etc., that render the calculation analytically tractable, but numerically uncertain. Powerful numerical path-integral methods have become available in recent years that allow the assessment of the accuracy of the various approximate methods. We compare several methods of computing f and [eta] to determine their applicability to various classes of particle shapes.