According to amputees, sensory feedback is amongst the most important features lacking from commercial prostheses. Although restoration of touch by means of implantable neural interfaces has been achieved, these approaches require surgical interventions, and their long-term usability still needs to be fully investigated. Here, we developed a non-invasive alternative which maintains some of the advantages of invasive approaches, such as a somatotopic sensory restitution scheme. We used transcutaneous electrical nerve stimulation (TENS) to induce referred sensations to the phantom hand of amputees. These sensations were characterized in four amputees over two weeks. Although the induced sensation was often paresthesia, the location corresponded to parts of the innervation regions of the median and ulnar nerves, and electroencephalographic (EEG) recordings confirmed the presence of appropriate responses in relevant cortical areas. Using these sensations as feedback during bidirectional prosthesis control, the patients were able to perform several functional tasks that would not be possible otherwise, such as applying one of three levels of force on an external sensor. Performance during these tasks was high, suggesting that this approach could be a viable alternative to the more invasive solutions, offering a trade-off between the quality of the sensation, and the invasiveness of the intervention.