Assuming you have a single element antenna (half or quarter wave patch, half wave dipole, quarter wave monopole, PIFA, etc), it can be done. Such antennas behave more or less as a series or parallel resonant circuit around the center frequency.
If your antenna is matched (so S11 goes through the center of the Smith Chart, or VSWR=1 at center frequency), it is very easy.
The VSWR = 2 bandwidth equals 71% of impedance bandwidth. So if you have an antenna with 30 MHz bandwidth (VSWR=2) at a center frequency of 1000 MHz, the impedance bandwidth = 30*1.41 = 42.4 MHz You may know that Q = (center frequency)/(3 dB impedance bandwidth), so in this case:
Q = 1000/42.4 = 24.
Note that this procedure only works when the VSWR at the center frequency is low (that means there is a good match).
If your antenna has zero imaginary part (so Im(Z)=0 ), but isn't 50 Ohms in simulation, just change the reference impedance so that the impedance curve goes through the center of the Smith Chart. Now locate the frequency points where |S11| = 0.3333. The difference between the corresponding frequencies is the bandwidth for VSWR=2. Now you can proceed as shown in the example.
Note that if there are lossy structues between the actual antenna and the point of measurement (or simulation), you will arrive at a Q-factor that is too low.
There are other solutions for determining Q-factor based on impedance, also for cases where the antenna impedance isn't real.