This paper analyses optimal investments in innovation when dealing with a stringent climate target and with the uncertain effectiveness of R&D. The innovation needed to achieve the deep cut in emissions is modelled by a backstop carbon-free technology whose cost depends on R&D investments. To better represent the process of technological progress, we assume that R&D effectiveness is uncertain. By means of a simple analytical model, we show how accounting for the uncertainty that characterizes technological advancement yields higher investments in innovation and lower policy costs. We then confirm the results via a numerical analysis performed with a stochastic version of WITCH, an energy-economy-climate model. The results stress the importance of a correct specification of the technological change process in economy-climate models.