Microring optical resonators have important applications in integrated photonic circuits for optical communications. We have developed two methods to fabricate polymer microring devices based on the nanoimprint technique. The first method uses a hard mold to directly imprint a polymer film to form optical waveguides in microring devices. We have demonstrated polymethylmethacrylate, polystyrene, and polycarbonate microring resonators fabricated using this technique. The second method employs a template filling approach, which allows a thicker waveguide to be fabricated; as well as polymers that are difficult to directly imprint. Optical filtering behavior of a microring resonator is demonstrated with a Q factor as high as 5800. The technique developed in this work could offer a cost-effective method to fabricate integrated photonic circuits based on polymer microring resonators.