We investigated the question of how the perception of three-dimensional information reconstructed numerically from digital holograms of real-world objects, and presented on conventional displays, depends on motion and stereoscopic presentation. Perceived depth in an adjustable random pattern stereogram was matched to the depth in hologram reconstructions. The objects in holograms were a microscopic biological cell and a macroscopic metal coil. For control, we used real physical objects in additional to hologram reconstructions of real objects. Stereoscopic presentation increased perceived depth substantially in comparison to non-stereoscopic presentation. When stereoscopic cues were weak or absent e.g. because of blur, motion increased perceived depth considerably. However, when stereoscopic cues were strong, the effect of motion was small. In conclusion, for the maximization of perceived three-dimensional information of holograms on conventional displays, it seems highly beneficial to use the combination of motion and stereoscopic presentation.