A novel methodology for designing Chipless Radio Frequency Identification (RFID) tags realized using the Additive Manufacturing technologies and exhibiting a high number of identification states is proposed and investigated. An encoding scheme based on the resonances and anti-resonances of the input impedance of the resonator is employed for identifying the tag, which is achieved by exploiting the set of zero-crossing points of the tag reactance. A tolerance analysis is also performed to avoid any ambiguity in the reading process and to minimize the redundancy, thus providing unique electromagnetic signatures which are also suitable for anti-counterfeiting applications. Several prototypes have been fabricated and tested to assess the practical implementation of the proposed encoding scheme.