The detection of benzonitrile (C6H5CN), 1- and 2-cyano-naphthalene (C10H7CN) in the cold, dark molecular cloud TMC-1 at centimetre (cm) wavelengths has opened up prospects for the detection of other N- and CN-containing polycyclic aromatic hydrocarbons (PAHs). In this light, the pure rotational spectra of N-pyrene (C15H9N), CN-pyrene (C15H9CN), N-coronene (C23H11N) and CN-coronene (C23H11CN) are reported here for the first time. The B3LYP/6-311+G(d,p) level of theory, in the Density Functional Theory (DFT) calculations, achieves the best performance for calculating the spectroscopic parameters and simulating the rotational spectra. The large permanent dipole moment of CN-PAHs makes them the most suitable PAH species for detection in the interstellar medium. Additionally, pyrene’s smaller partition function makes CN-pyrene a prime candidate to be discovered in cold, dark molecular clouds such as the TMC-1. The present work sets a benchmark for theoretical rotational spectra of N- and CN-containing PAHs and may act as a guide for laboratory experiments and observational searches.