  We consider a smooth interface between a topological nodal-line semimetal and
a topologically trivial insulator (e.g., the vacuum) or another semimetal with
a nodal ring of different radius. Using a low-energy effective Hamiltonian
including only the two crossing bands, we show that these junctions accommodate
a two-dimensional zero-energy level and a set of two-dimensional dispersive
bands, corresponding to states localized at the interface. We characterize the
spectrum, identifying the parameter ranges in which these states are present,
and highlight the role of the nodal radius and the smoothness of the interface.
We also suggest material-independent ways to detect and identify these states,
using optical conductivity and infrared absorption spectroscopy in magnetic
field.
