Why do we need to calculate the resonant frequency for antennas?
Antennas at 13.56 MHz are usually used for near field communication. This is dominated by inductive coupling and, to make life easier on the "driving" transmitter electronics, a capacitor is added to make it electrically resonant. This helps the electronics produce a bigger magnetic field and additionally it acts like a filter so that spurious harmonics are substantially removed thus reducing EMI.

Making it resonant like this makes the antenna purely (or very nearly) resistive even when the remote RFID device is getting quite close.

If the antenna is in fact a regular EM antenna then the word "resonate" can take on a subtly different meaning. In this example resonating the antenna means matching its size so that it produces an electric field 377 times bigger than the magnetic field (hence Jim's comment). But what is this magical number you might ask - it's the impedance of free space governed by \$\epsilon_0\$ and \$\mu_0\$. These parameters define the speed of light in a vacuum and the speed of an EM wave but, their ratio defines the impedance of free space.

So, given that our antenna needs to emit individual E and H fields at the right ratio for maximizing transmission distance, we make the length of an antenna optimized for this. Having said this, it doesn't mean that electrically the antenna looks like a resistor: -



The above is for a dipole antenna and it is usually made to be half a wavelength long. Looking at it from an electrical standpoint yields an impedance of 73 + j43 Ohms. In other words it can be electrically optimized by cancelling the imaginery (inductive) term with a capacitor. Or, just operate with it slightly less than 0.5 wavelengths and get a purely resistive impedance of ~70 ohms. Reference reading from antenna-theory.com

So, in short, making an antenna resonate can mean different things to different folk.