The vestigial signal defence (VSD) method is used widely for GNSS spoofing detection through monitoring the vestigial signals within the receiver. Though the VSD has been extensively investigated in the open literature, its sensitivity in terms of detection and false alarm probabilities has not been analysed. This is addressed in this study. The sensitivity models including the vestigial signal-to-interference and noise ratio (SINR) and the detection and false alarm probabilities are mathematically formulated. The models are used to quantify and characterise the SINR and the detection and false alarm probabilities. It shows that the VSD is vulnerable to relatively strong spoofing signals. Strong spoofing signals significantly increase the noise floor in turn greatly decreasing the vestigial SINR, resulting in an unacceptable VSD detection performance. It also shows that the sensitivity could be improved with a higher sampling frequency and a longer integration time. It is therefore recommended to use a scheme that combines a long integration time and noise floor monitoring. The sensitivity models together with the recommendation scheme are validated by simulation.