The Solar Orbiter mission, with an orbit outside the Sun-Earth line and leaving the ecliptic plane, opens up opportunities for the combined analysis of measurements obtained by solar imagers and spectrometers. For the first time, different spectrometers will be located at wide angles to each other, allowing three-dimensional (3D) spectroscopy of the solar atmosphere. Here we develop a methodology to prepare for this kind of analysis, by using data from the Hinode mission and the Solar Dynamics Observatory, respectively. We employ solar rotation to simulate measurements of spectrometers with different views of the solar corona. The resulting data allow us to apply stereoscopic tie-pointing and triangulation techniques designed for the STEREO spacecraft pair, and to perform 3D analysis of the Doppler shifts of a quasi-stationary active region. Our approach allows the accurate reconstruction of 3D velocity vectors in plasma flows along “open” and “closed” magnetic loops. This technique will be applied to the actual situation of two spacecraft at different separations with spectrometers on board (the Solar Orbiter Spectral Imaging of the Coronal Environment versus the Interface Region Imaging Spectrograph (IRIS) and Hinode imaging spectrometer) and we summarise how these observations can be coordinated to assess vector velocity measurements. This 3D spectroscopy method will facilitate the understanding of the complex flows that take place throughout the solar atmosphere.