We report on the implemented design of a two-colour instrument based on electron-multiplying CCD (EMCCD) detectors. This instrument is currently installed at the Danish 1.54 m telescope at ESO's La Silla Observatory in Chile, and will be available at the SONG (Stellar Observations Network Group) 1m telescope node at Tenerife and at other SONG nodes as well. We present the software system for controlling the two-colour instrument and calibrating the high frame-rate imaging data delivered by the EMCCD cameras. An analysis of the performance of the Two-Colour Instrument at the Danish telescope shows an improvement in spatial resolution of up to a factor of two when doing shift-and-add compared with conventional imaging, and the possibility of doing high-precision photometry of EMCCD data in crowded fields. The Danish telescope, which was commissioned in 1979, is limited by a triangular coma at spatial resolutions below 0.5 arcsec, and better results will thus be achieved at the near diffraction-limited optical system on the SONG telescopes, where spatial resolutions close to 0.2 arcsec have been achieved. Regular EMCCD operations have been running at the Danish telescope for several years and produced a number of scientific discoveries, including microlensing detected exoplanets, detecting previously unknown variable stars in dense globular clusters, and discovering two rings around the small asteroid-like object (10199) Chariklo. Based on data collected with the Danish 1.54m telescope at ESO's La Silla Observatory.