Nowadays only few examples of the attractive classical stone architecture remain standing, since the historic settlements of the populations which have built them, were often located in areas of severe seismicity. The interest of the scientific community in the conservation of these important historical structures is in continual increase. The main difficulty resides in improving the seismic strength by preserving the cultural heritage at the same time; in summary non-invasive strengthening methods are requested. The suggested possibility is the Tendon System: a passive structural control technique. The basic idea is to tie the loose stone blocks of a historical monument with tendons that run through their centres. Ideally, no pre-stressing is applied. Only during motions under earthquakes, forces are developed in the tendons that limit these motions and prevent collapse. The work describes this control approach applied to Greek columns. In particular, seismic behaviour of columns controlled by means of tendons is presented by analytical formulations. These analytical results are then confirmed by preliminary experimental tests carried out on scaled models on a small shaking table.