The Extant Phylogenetic Bracket approach is applied to infer the kind of soft tissue that would have been associated with the bifurcated neural spines of the cervical vertebrae of sauropods. A median ligament (“ligamentum nuchae” or lig. supraspinale) extends along the tips of the neural spines and attaches to them in the cervical region of extant avian and non-avian diapsids, thus enabling a parsimonious inference that a homologous ligament would also have attached to the same sites in extinct diapsids, including sauropods. In the extant ratite bird, Rhea americana, “lig. nuchae” splits ventrally into two halves as the neural spines become bifurcated in the posterior cervical region, thereby maintaining its connection to both tips of each bifurcated neural spine. This shows the conservative nature of the connection between “lig. nuchae” and its osteological correlate. Furthermore, this ligament and the notches of the bifurcated neural spines enclose another ligament, lig. elasticum interspinale, that arises from the non-bifid neural spine of the most posterior “cervico-dorsal” and gives off branches inserting on the posterior surfaces of the neural spines of the middle to posterior cervicals in Rhea. This ligament in Rhea is suggested to be a good modern analog to the structure occupying the notches of the bifurcated neural spines of sauropods. A hypothetical reconstruction of the proposed ligament system is given using Camarasaurus and Apatosaurus as examples.