Estimating the bandwidth of various signals
Another way would be fitting each of your signals' PSD with a Gaussian probability density function whose standard deviation $\sigma$ and mean $\mu$ you estimate, and use the full width at half maximum (FWHM) of this approximation as your half-power bandwidth. This is known accurately with the following closed form:
$$
\mathrm{FWHM}=2\sqrt{2\ln(2)} \sigma\approx 2.355\sigma
$$ 
This approach is often used in practice to measure things like bandwidth expansion.