Granular jamming is a popular soft robotics technology that has seen recent widespread applications including industrial gripping, surgical robotics and haptics. However, to date the field has not fully exploited the fundamental science of the jamming phase transition, which has been rigorously studied in the field of statistical and condensed matter physics. This work introduces vibration as a means to improve the properties of granular jamming grippers through vibratory fluidisation and the exploitation of resonant modes within the granular material. We show that vibration in soft jamming grippers can improve holding strength, reduce the downwards force needed for the gripping action, and lead to a simplified setup where the second air pump, generally used for unjamming, could be removed. In a series of studies, we show that frequency and amplitude of the waveforms are key determinants to performance, and that jamming performance is also dependent on temporal properties of the induced waveform. We hope to encourage further study in transitioning fundamental jamming mechanisms into a soft robotics context to improve performance and increase diversity of applications for granular jamming grippers.