Bandwidth of metamaterial are always analyzed by using simulation method. Software like COMSOL, CST and FDTD simulations are widely used.

The bandwidth of metamaterial is directly associated with its structure parameters and  component materials. for specific frequency band designs: 1. Choosing suitable material, for example, Au and silicon are widely used for metamaterial designs in infrared while Ag and Al is widely used for metamaterial designs in visible wavelengths. 2. Designing and optimizing the structures to realize the proposed function in specific frequency band. Following previous works is an effective way for structure design.

In case of metamaterial absorbers, it is specified interms of full width half maximum bandwidth(FWHM)-it specifies the frequency range in which the absorbptivity is equal to or more than 50%.

Hi,

Bandwidth =( max. freq. - min. freq.)/ (square root of (max. freq, x min. freq.),

There are lots of paper which might be helpful for you.

1)Metamaterial Extends Patch Antenna Bandwidth

2)A frequency and bandwidth tunable metamaterial absorber in x-band

Thanks,

All the best,