The viscoelastic behavior of semiflexible macromolecules is studied using a trumbbell model with variable flexibility at the central hinge. The frequency-dependent solution viscosity for that model is calculated from Brownian dynamics simulations. The Green-Kubo formula is used to calculate the viscosity from flow-free Brownian trajectories. First, we obtain overall macromolecular properties such as the zero-shear intrinsic viscosity, longest relaxation times for viscoelasticity and for reorientation of the end-to-end vector, and others. We also calculate curves for the frequency dependence of the dynamic moduli. The results are compared with the existing theories of Roitman and Zimm and of Nagasaka and Yamakawa. Of particular interest is the determination of the range of flexibility for which the latter (which includes the effects of hydrodynamic interaction) is valid. Finally, we discuss the way in which hydrodynamic interaction influences the viscoelastic behavior of semiflexible macromolecules.