A significant part of barred disc galaxies exhibits boxy/peanut-shaped structures (B/PS bulges) at high inclinations. Another structure also associated with the bar is a barlens, often observed in galaxies in a position close to face-on. At this viewing angle, special kinematic tests are required to detect a 3D extension of the bars in the vertical direction (B/PS bulges). We use four pure N-body models of galaxies with B/PS bulges, which have different bar morphology from bars with barlenses to the so-called face-on peanut bars. We analyse the kinematics of our models to establish how the structural features of B/PS bulges manifest themselves in the kinematics for galaxies at intermediate inclinations and whether these features are related to the barlenses. We apply the dissection of the bar into different orbital groups to determine which of them are responsible for the features of the LOSVD (line-of-sight velocity distribution), i.e. for the deep minima of the h4 parameter along the major axis of the bar. As a result, we claim that for our models at the face-on position, the kinematic signatures of a ‘peanut’ indeed track the vertical density distribution features. We conclude that orbits responsible for such kinematic signatures differ from model to model. We pay special attention to the barlens model. We show that orbits assembled into barlens are not responsible for the kinematic signatures of B/PS bulges. The results presented in this work are applicable to the interpretation of IFU observations of real galaxies.