We present predictive multiscale models of the multiaxial strain-sensing response of conductive CNT-polymer composites. Detailed physically-based finite element (FE) models at the micron scale are used to produce training data for an artificial neural network; the latter is then used, at macroscopic scale, to predict the electro-mechanical response of components of arbitrary shape subject to a non-uniform, multiaxial strain field, allowing savings in computational time of six orders of magnitude. We apply this methodology to explore the application of CNT-polymer composites to the construction of different types of sensors and to damage detection.