We discuss the design, fabrication, and characterization of silicon-nitride microring resonators for nonlinear-photonic and biosensing device applications. The first part presents new theoretical and experimental results that overcome highly normal dispersion of silicon-nitride microresonators by adding a dispersive coupler. The latter parts review our work on highly efficient second-order nonlinear interaction in a hybrid silicon-nitride slot waveguide with nonlinear polymer cladding and silicon-nitride microring application as a biosensor for human stress indicator neuropeptide Y at the nanomolar level.