Brain decoding algorithms form an important part of the arsenal of analysis tools available to neuroscientists, allowing for a more detailed study of the kind of information represented in patterns of cortical activity. While most current decoding algorithms focus on estimating a single, most likely stimulus from the pattern of noisy fMRI responses, the presence of noise causes this estimate to be uncertain. This uncertainty in stimulus estimates is a potentially highly relevant aspect of cortical stimulus processing, and features prominently in Bayesian or probabilistic models of neural coding. Here, we focus on sensory uncertainty and how best to extract this information with fMRI. We first demonstrate in simulations that decoding algorithms that take into account correlated noise between fMRI voxels better recover the amount of uncertainty (quantified as the width of a probability distribution over possible stimuli) associated with the decoded estimate. Furthermore, we show that not all correlated variability should be treated equally, as modeling tuning-dependent correlations has the greatest impact on decoding performance. Next, we examine actual noise correlations in human visual cortex, and find that shared variability in areas V1-V3 depends on the tuning properties of fMRI voxels. In line with our simulations, accounting for this shared noise between similarly tuned voxels produces important benefits in decoding. Our findings underscore the importance of accurate noise models in fMRI decoding approaches, and suggest a statistically feasible method to incorporate the most relevant forms of shared noise.