Context. The astrophysical relevance of the fluoromethylidynium ion and its importance for the interstellar chemistry of fluorine motivated the present laboratory spectroscopic investigation of both 12 CF + and the corresponding 13 C-containing isotopologue, 13 CF + . Aims. This investigation has been carried out to provide accurate rest frequencies for future (radioastronomical) observations, to improve the accuracy of the values for the spectroscopic parameters available in the literature for CF + , and to provide them for the first time for 13 CF + . Methods. Rotational spectra of CF + and 13 CF + were recorded in the millimeter-and submillimeter-wave frequency ranges. Their investigation was supplemented by high-level quantum-chemical computations using state-of-the-art coupled-cluster techniques. Results. We report the most accurate ground-state rotational parameters available so far for CF + and 13 CF + . Conclusions. The ground-state rotational parameters as well as the rest frequencies of 13 CF + will be useful for future observational purposes with the aim of improving the knowledge of fluorine interstellar chemistry.