This paper presents a design methodology for suppressing spurious frequencies in dual-band bandstop filters. Traditional methods used for suppression of spurious frequency for bandpass filter are not effective for bandstop filters. Two techniques are discussed in this paper for achieving spurious response suppression in bandstop filters. With the first technique, the spurious response is pushed to a higher frequency expanding the useable band, while with the second proposed technique spurious response is suppressed for dual-band bandstop filters. Initially, a bandstop filter with dual operating frequencies at 1.5 GHz and 2.6 GHz is designed and both techniques discussed in the paper are used to suppress the spurious response.