Abstract Pulsar timing array collaborations, such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), are seeking to detect nanohertz gravitational waves emitted by supermassive black hole binaries formed in the aftermath of galaxy mergers. We have searched for continuous waves from individual circular supermassive black hole binaries using NANOGrav’s recent 12.5 yr data set. We created new methods to accurately model the uncertainties on pulsar distances in our analysis, and we implemented new techniques to account for a common red-noise process in pulsar timing array data sets while searching for deterministic gravitational wave signals, including continuous waves. As we found no evidence for continuous waves in our data, we placed 95% upper limits on the strain amplitude of continuous waves emitted by these sources. At our most sensitive frequency of 7.65 nHz, we placed a sky-averaged limit of h ₀ < (6.82 ± 0.35) × 10⁻¹⁵, and h ₀ < (2.66 ± 0.15) × 10⁻¹⁵ in our most sensitive sky location. Finally, we placed a multimessenger limit of  < ( 1.41 ± 0.02 ) × 10 9 M ⊙ on the chirp mass of the supermassive black hole binary candidate 3C 66B.