Foundation models are trained on vast amounts of data at scale using self-supervised learning, enabling adaptation to a wide range of downstream tasks. At test time, these models exhibit zero-shot capabilities through which they can classify previously unseen (user-specified) categories. In this paper, we address the problem of quantifying uncertainty in these zero-shot predictions. We propose a heuristic approach for uncertainty estimation in zero-shot settings using conformal prediction with web data. Given a set of classes at test time, we conduct zero-shot classification with CLIP-style models using a prompt template, e.g., ``an image of a '', and use the same template as a search query to source calibration data from the open web. Given a web-based calibration set, we apply conformal prediction with a novel conformity score that accounts for potential errors in retrieved web data. We evaluate the utility of our proposed method in Biomedical foundation models; our preliminary results show that web-based conformal prediction sets achieve the target coverage with satisfactory efficiency on a variety of biomedical datasets.