Compressive sensing is a new data compression paradigm that has shown significant promise in fields such as MRI. However, the practical performance of the theory very much depends on the characteristics of the signal being sensed. As such the utility of the technique cannot be extrapolated from one application to another. Electroencephalography (EEG) is a fundamental tool for the investigation of many neurological disorders and is increasingly also used in many non-medical applications, such as Brain-Computer Interfaces. This paper characterises in detail the practical performance of different implementations of the compressive sensing theory when applied to scalp EEG signals for the first time. The results are of particular interest for wearable EEG communication systems requiring low power, real-time compression of the EEG data.