Recovery of reaching and grasping ability is the priority for people with cervical spinal cord injury (SCI). Epidural electrical stimulation (EES) has shown promising results in improving motor control after SCI in various animal models and in humans. Notably, the application of stimulation bursts with spatiotemporal sequences that reproduce the natural activation of motoneurons restored skilled leg movements in rodent and nonhuman primate models of SCI. Here, we studied whether this conceptual framework could be transferred to the design of cervical EES protocols for the recovery of reaching and grasping in nonhuman primates. We recorded muscle activity during a reaching and grasping task in a macaque monkey and found that this task involves a stereotypical spatiotemporal map of motoneuron activation. We then characterized the specificity of a spinal implant for the delivery of EES to cervical spinal segments in the same animal. Finally, we combined these results to design a simple stimulation protocol that may reproduce natural motoneuron activation and thus facilitate upper limb movements after injury.