  We introduce two new extensions to the beam search algorithm based on
conformal predictions (CP) to produce sets of sequences with theoretical
coverage guarantees. The first method is very simple and proposes
dynamically-sized subsets of beam search results but, unlike typical CP
procedures, has an upper bound on the achievable guarantee depending on a
post-hoc calibration measure. Our second algorithm introduces the conformal set
prediction procedure as part of the decoding process, producing a variable beam
width which adapts to the current uncertainty. While more complex, this
procedure can achieve coverage guarantees selected a priori. We provide
marginal coverage bounds for each method, and evaluate them empirically on a
selection of tasks drawing from natural language processing and chemistry.
