SPIRE, the Spectral and Photometric Imaging Receiver, will be a bolometer instrument for ESA's Herschel satellite. The instrument comprises a three-band imaging photometer covering the 250-500 μm range, and an imaging Fourier Transform Spectrometer (FTS) covering 200-670 μm. This paper presents the requirements for and design of the photometer and spectrometer calibration/illumination sources, and the results of laboratory tests on prototypes. The photometer calibrator is an electrically heated thermal source of submillimetre radiation, the purpose of which is to provide a repeatable signal for in-flight monitoring of health and responsivity of the SPIRE photometer detectors. It is not required to provide absolute calibration or uniform illumination of the arrays, but it may be used as part of the overall calibration scheme. The spectrometer calibrator is located at a pupil at the second input port of the FTS. It is designed to enable matching of the telescope emission for a range of telescope temperature (60-90 K) and emissivity (2% - 10%). By matching the telescope emission at this port, the high background from the Herschel telescope emission can be nulled to a high degree, resulting in an interferogram in which the contribution from the astronomical source is not overwhelmed by the telescope offset. The flexibility for telescope matching inherent in the design is important, as the exact telescope parameters will be unknown until the satellite is in operation. The FTS calibrator will also be used to assist in the absolute calibration scheme for SPIRE FTS observations.