what's all this about...

SWR greater than 1:1 will affect how much power a Common Mode Choke can handle because it increases the magnitude of the voltage and current peaks along the feedline.  

This increases stress on the choke in two ways:

    1) Instantaneous voltage and current experienced by the coax windings will increase

    2) Power dissipation in the choke will increase 

Instantaneous Power Limits:  

The peak voltage inside a perfectly matched coax with 1500 watts applied will be 386 volts. However, any SWR higher than 1:1 will increase that peak voltage by the SWR ratio.  So if the SWR is 3:1, the peak voltage will be 3 x 386 = 1158 volts.  

The RG400 coax used to wind our chokes is rated for a maximum peak of 2400 volts. This creates an "absolute maximum instantaneous power limit". If everything is perfectly matched, this translates into 9.3 kW (but the choke will be limited by other factors before that power level is reached). More practically, it also means that the maximum SWR the choke can handle when 1500 watts of power is applied is about 6:1.

Common Mode Chokes are intended to be used in well matched 50 ohm systems. If an antenna is poorly matched, generating high SWR ratios, a matching network or impedance transformer should be employed so that the choke is not subjected to high SWR ratios and high power.  

So peak voltage is not usually the determining factor for choke power limits.

Similarly, peak current in the coax is increased by the SWR ratio. Peak current when 1500 watts of power is applied to a perfectly matched load will be about 7.75 amps. So, again, an SWR of 3:1 will increase that peak current to about 23 amps. That's a lot, but not enough to damage the coax directly.  

Power Dissipation:  The most important effect of increased SWR is the increase in power dissipation in the choke. Inherent Loss (dissipative portion of insertion loss) in a common mode choke is due to loss in the coax used to wind the choke. Higher current in the coax due to raised SWR will cause increased dissipation in the choke. This dissipation will cause additional heating, which ultimately limits the power a choke can handle.

For these reasons, it is best practice to match the antenna system reasonably well before the Common Mode Choke. 

Location of the choke: Since the coax inside our chokes is relatively short, only a fraction of a wavelength, the power dissipated in it is controlled by its location along the feedline relative to standing wave current peaks. Because we can't really control this location, especially in the case of multiband antennas, we must assume the worst and count on the choke catching a current peak.