We present a first-principles study of bare and hydrogen passivated armchair nanoribbons of the puckered single layer honeycomb structures of silicon and germanium. Our study includes optimization of atomic structure, stability analysis based on the calculation of phonon dispersions, electronic structure, and the variation in band gap with the width of the ribbon. The band gaps of silicon and germanium nanoribbons exhibit family behavior similar to those of graphene nanoribbons. The edges of bare nanoribbons are sharply reconstructed, which can be eliminated by the hydrogen termination of dangling bonds at the edges. Periodic modulation of the nanoribbon width results in a superlattice structure which can act as a multiple quantum well. Specific electronic states are confined in these wells. Confinement trends are qualitatively explained by including the effects of the interface. In order to investigate wide and long superlattice structures we also performed empirical tight-binding calculations with parameters determined from ab initio calculations.