A certificate for interstellar service was a legal document issued by a physician certifying that the individual named in the document met the required medical criteria for service on a starship.
Starfleet required such certification of its personnel. The certificate needed to indicate that the individual met certain cardiovascular, metabolic, and cognitive requirements.
In 2399, the retired Admiral Jean-Luc Picard asked Dr. Moritz Benayoun to issue him such a certificate in preparation for reentering Starfleet, on the basis of a remote medscan. Benayoun noted that Picard met or exceeded all the required criteria, despite his age, but a small defect in his parietal lobe was growing worse and would eventually lead to a fatal condition. Nevertheless, Benayoun issued the certificate, noting that whatever Picard wanted to do, perhaps it would kill him before the fatal condition began to affect him. (PIC: "Maps and Legends")