Seven-stone antas are a group of megalithic monuments that were built in the southwest of the Iberian Peninsula for a period of some one thousand years in the 4th millennium B.C. They were constructed with a pattern of orientations that certainly situate them among the oldest monuments on Earth with undisputable astronomical orientations. They were built in an extended area of the present day regions of Alentejo, in Portugal and Extremadura, in Spain. The presence of such impressive, extremely old monuments at both sides of the Spanish-Portuguese frontier and their reliability as an extremely important Case Study for the UNESCO Astronomical Heritage initiative makes of this particular set of megalithic tombs a good opportunity as a paradigm for serial nominations. We believe that seven-stone antas as a group, and especially a particularly well-preserved set of them in the area of Valencia de Alcántara (Spain) and central Alentejo (Portugal), deserve recognition within the framework of the astronomical world heritage initiative. This would certainly serve for guarantee the protection of the sites for any possible challenge in the future and for gaining a deserved recognition among society. Interestingly, at the other extreme of the Mediterranean, in the Transjordan plateau there are some of the largest and most attractive groups of dolmens of the Levant, fully comparable to the best western exemplars. The orientations of 180 dolmens were measured, allowing the study of the astronomical aspect of the megalithic phenomena in the region. In this case, EBA populations orientated their tombs according to the sky, providing a 2nd potential case for serial nomination. However, in contrast to Iberia, we should stress that it is especially troubling that specialists in the Levant are now faced with the rapid destruction of Jordan’s megalithic heritage due to the huge quarries that are expanding as a plague. It is indeed necessary to increase the interest through UNESCO promotion on these beautiful and extremely interesting monuments. They may be seriously protected as soon as possible by local authorities before it is too late.