If you are measuring power (not amplitude), 3 dB is approximately one half. So if you plot power as a function of frequency (perhaps on a log-log plot), and find that the peak has a value of, say, PeakValue, then the ±3 dB points will be where the Gaussian curve you fit has the value of PeakValue/2 (one to the left of the peak, one to the right).
Bob Schor