Cyanamide is one of the few interstellar molecules containing two chemically different N atoms. It was detected recently toward the solar-type protostar IRAS 16293-2422 B together with H$_2$N$^{13}$CN and HDNCN in the course of the Atacama Large Millemeter/submillimeter Array (ALMA) Protostellar Interferometric Line Survey (PILS). The detection of the 15N isotopomers or the determination of upper limits to their column densities was hampered by the lack of accurate laboratory data at the frequencies of the survey. We wanted to determine spectroscopic parameters of the $^{15}$N isotopomers of cyanamide that are accurate enough for predictions well into the submillimeter region and to search for them in the PILS data. We investigated the laboratory rotational spectra of H$_2^{15}$NCN and H$_2$NC$^{15}$N in the selected region between 192 and 507~GHz employing a cyanamide sample in natural isotopic composition. Additionally, we recorded transitions of H$_2$N$^{13}$CN. We obtained new or improved spectroscopic parameters for the three isotopic species. Neither of the $^{15}$N isotopomers of cyanamide were detected unambiguously in the PILS data. Two relatively clean lines can be tentatively assigned to H$_2^{15}$NCN. If confirmed, their column densities would imply a low $^{14}$N/$^{15}$N ratio for cyanamide toward this source. The resulting line lists should be accurate enough for observations up to about 1 THz. More sensitive observations, potentially at different frequencies, may eventually lead to the astronomical detection of these isotopic species.Read less <