Certain shift operator induced finite-dimensional approximations of an important class of delay systems are studied. H-infinity, H-2, and L-1 error bounds are given for stable delay systems. Furthermore, a multiple shift formula, generated by a second-order Pade shift, is analyzed further, and an exact asymptotic H-infinity error formula is derived. The studied class of shift operator induced approximations provides an appealing and most transparent approach for determining good finite-dimensional models of delay systems.