Keyword localisation is the task of finding where in a speech utterance a given query keyword occurs. We investigate to what extent keyword localisation is possible using a visually grounded speech (VGS) model. VGS models are trained on unlabelled images paired with spoken captions. These models are therefore self-supervised -- trained without any explicit textual label or location information. To obtain training targets, we first tag training images with soft text labels using a pretrained visual classifier with a fixed vocabulary. This enables a VGS model to predict the presence of a written keyword in an utterance, but not its location. We consider four ways to equip VGS models with localisations capabilities. Two of these -- a saliency approach and input masking -- can be applied to an arbitrary prediction model after training, while the other two -- attention and a score aggregation approach -- are incorporated directly into the structure of the model. Masked-based localisation gives some of the best reported localisation scores from a VGS model, with an accuracy of 57% when the system knows that a keyword occurs in an utterance and need to predict its location. In a setting where localisation is performed after detection, an $F_1$ of 25% is achieved, and in a setting where a keyword spotting ranking pass is first performed, we get a localisation P@10 of 32%. While these scores are modest compared to the idealised setting with unordered bag-of-word-supervision (from transcriptions), these models do not receive any textual or location supervision. Further analyses show that these models are limited by the first detection or ranking pass. Moreover, individual keyword localisation performance is correlated with the tagging performance from the visual classifier. We also show qualitatively how and where semantic mistakes occur, e.g. that the model locates surfer when queried with ocean.