Why can't you put a plane under a trace antenna?
An antenna converts a low impedance transmission line (from the chip or also via a coax or stripline) to a high impedance at the end of the antenna. The high impedance is to suit the impedance of free space (377 or 120\$\pi\$ ohms). An antenna does this gently and in doing so creates a standing wave along its length in order to allow the current to gently fall to zero at the end (such as in a quarter wave monopole) whilst the voltage reaches a maximum thus, the correct ratio of E field to H field is created (a ratio which defines the impedance of free space i.e. 377 ohms).

Generally, the near-field extends to one wavelength and anything in the vicinity can prevent the above happening effectively. If you just have a track above an earth plane you are going to create a sudden discontinuity (at the end) and get a total reflection of power back to the transmitter with no power being emitted into space. That's not an EM antenna.


  I'm working with RFID for the first time.


Given this, you may actually be using an "antenna" where the dominant field is magnetic and there are plenty of things you can do that you cannot do if you were using an EM transmission to transmit power. So, quit the generalized hand waving in your question and get specific - what operating frequency and what antenna design have you targeted?