We search for ‘solar twins’ in the Geneva–Copenhagen Survey (GCS) using high-resolution optical spectroscopy. We initially select Sun-like stars from the GCS by absolute magnitude, (b − y) colour and metallicity close to the solar values. Our aim is to find the stars which are spectroscopically very close to the Sun using line depth ratios and the median equivalent widths and depths of selected lines with a range of excitation potentials. We present the 10 best stars fulfilling combined photometric and spectroscopic criteria, of which six are new twins. We use our full sample of Sun-like stars to examine the calibration of the metallicity and temperature scale in the GCS. Our results give rise to the conclusion that the GCS may be offset from the solar temperature and metallicity for Sun-like stars by 100 K and 0.1 dex, respectively.