In information retrieval (IR), candidate set pruning has been commonly used to speed up two-stage relevance ranking. However, such an approach lacks accurate error control and often trades accuracy off against computational efficiency in an empirical fashion, lacking theoretical guarantees. In this paper, we propose the concept of certified error control of candidate set pruning for relevance ranking, which means that the test error after pruning is guaranteed to be controlled under a user-specified threshold with high probability. Both in-domain and out-of-domain experiments show that our method successfully prunes the first-stage retrieved candidate sets to improve the second-stage reranking speed while satisfying the pre-specified accuracy constraints in both settings. For example, on MS MARCO Passage v1, our method yields an average candidate set size of 27 out of 1,000 which increases the reranking speed by about 37 times, while the MRR@10 is greater than a pre-specified value of 0.38 with about 90% empirical coverage and the empirical baselines fail to provide such guarantee. Code and data are available at: https://github.com/alexlimh/CEC-Ranking.