We present Hinted Networks: a collection of architectural transformations for improving the accuracies of neural network models for regression tasks, through the injection of a prior for the output prediction (i.e. a hint). We ground our investigations within the camera relocalization domain, and propose two variants, namely the Hinted Embedding and Hinted Residual networks, both applied to the PoseNet base model for regressing camera pose from an image. Our evaluations show practical improvements in localization accuracy for standard outdoor and indoor localization datasets, without using additional information. We further assess the range of accuracy gains within an aerial-view localization setup, simulated across vast areas at different times of the year.