The radiative forcing of contrails is quantified for a hypothetical fleet of cryoplanes in comparison with a conventional aircraft fleet. The differences in bulk optical properties between conventional and cryoplane contrails are determined by numerical simulations of the microphysical evolution of conventional and cryoplane contrails, under several ambient conditions. Both types of contrails contain about the same ice mass, but the mean effective particle radius is found to be smaller by about a factor of 0.3 in conventional contrails than in cryoplane ones. Hence, in case of cryoplanes the contrail optical depth is lower, which counteracts (with respect to radiative forcing) the effect of increased contrail cover due to the higher specific emission of water vapour. If the information gained from the microphysical simulations is translated to the framework of a global climate model, the global mean radiative forcing of cryoplane contrails is simulated to be between about 30% lower and 30% higher compared to the radiative forcing of conventional contrails, depending on the quantitative assumptions made for the mean particle properties and also depending on the time slice considered. Our results indicate that the effect of decreased optical depth is about the same magnitude as the effect of increased contrail cover. Current state of knowledge does not allow a conclusive assessment whether the net radiative impact of cryoplane contrails will be smaller or larger than that of conventional contrails. Uncertainty with respect to radiative forcing arises mainly from insufficient knowledge regarding the mean effective ice crystal radius for both conventional and, especially, cryoplane contrails.