How much current can you draw from a resonant loop antenna

In the case of a loop antenna that has uncancelled inductance, the magnetic field generated by the current in the antenna is in antiphase to the magnetic field of the incoming EM wave, so it is reasonable to believe that the antenna current that leads to cancellation of the incoming magnetic flux will be the maximum current.
But in the case of a resonant antenna, there is 90 degrees phase shift between the incoming magnetic field and the magnetic field generated by the antenna. In the idealized situation (zero resistive losses, neglecting the EM radiation by the receiving antenna) is there any limit on the current?

Theoretic there is no limit in the current due to EM coupling of antennas (or is a high limit).
In coupled transformers appear current limitation due to saturation of the magnetic core.