Context. Glycinamide (NH 2 CH 2 C(O)NH 2 ) is considered to be one of the possible precursors of the simplest amino acid glycine. Its only rotational spectrum reported so far has been in the cm-wave region on a laser-ablation generated supersonic expansion sample. Aims. The aim of this work is to extend the laboratory spectrum of glycinamide into the millimetre wave region to support its searches in the interstellar medium and to perform the first check for its presence in the high-mass star forming region Sagittarius B2(N). Methods. Glycinamide was synthesised chemically and was studied with broadband rotational spectroscopy in the 90-329 GHz region with the sample in slow flow at 50 • C. Tunneling across a low energy barrier between two symmetry equivalent configurations of the molecule resulted in splitting of each vibrational state and many perturbations in associated rotational energy levels, requiring careful coupled state fits for each vibrational doublet. We searched for emission of glycinamide in the imaging spectral line survey ReMoCA performed with the Atacama Large Millimetre/submillimetre Array toward Sgr B2(N). The astronomical spectra were analysed under the assumption of local thermodynamic equilibrium. Results. We report the first analysis of the mm-wave rotational spectrum of glycinamide, resulting in fitting to experimental measurement accuracy of over 1200 assigned and measured transition frequencies for the ground state tunneling doublet, of many lines for tunneling doublets for two singly excited vibrational states, and determination of precise vibrational separation in each doublet. We did not detect emission from glycinamide in the hot molecular core Sgr B2(N1S). We derived a column density upper limit of 1.5 × 10 16 cm −2 , which implies that glycinamide is at least seven times less abundant than aminoacetonitrile and 1.8 times less abundant than urea in this source. A comparison with results of astrochemical kinetics models for species related to glycinamide suggests that its abundance may be at least one order of magnitude below the upper limit obtained toward Sgr B2(N1S). This means that glycinamide emission in this source likely lies well below the spectral confusion limit in the frequency range covered by the ReMoCA survey. Conclusions. Thanks to the spectroscopic data provided by this study, the search for glycinamide in the interstellar medium can continue on a firm basis. Targetting sources with a lower level of spectral confusion, such as the Galactic Center shocked region G+0.693-0.027, may be a promising avenue.