Antenna systems for passive radio-frequency identification (RFID) tags. The antenna systems have a very small form factor with good power harvesting and good performance in proximity to other antennas. The antenna system includes at least one, and preferably two, parallel serpentine antenna elements formed on, or otherwise supported by, an antenna substrate so that a RFID-tag integrated circuit (IC) can be electrically contacted to the antenna system at one end of the antenna substrate. A conducting wire that runs in the same direction as the at least one serpentine antenna element is used to match impedance and enhance antenna performance and power flow between the antenna and the IC. An impedance-matching circuit may be employed in place of the conducting wire to facilitate impedance matching between the antenna and the IC.