An essential characteristic for unbiased and diligent information-seeking that can enable informed opinion formation and decision-making is intellectual humility (IH), the awareness of the limitations of one's knowledge and opinions. While researchers have recognized the potential to boost IH in individuals, the effect of such interventions on their search behavior, along with the broader significance of IH in the context of web search on debated topics remains unexplored. In this paper, we present the results of a preregistered user study (N = 299) that we conducted to (1) test the effect of three interventions that boost self-reported IH on opinionated individuals' search behavior and (2) explore the role of IH in the search process of opinionated individuals more broadly. IH-boosting interventions did not affect search behavior; we attribute this to the high familiarity of the search environment, prompting searchers to default to their usual search behavior. Still, explorations of the role of IH in the search process indicate that IH and IH-related search intentions should be considered as relevant factors in the pursuit of supporting unbiased and diligent search on debated topics. Based on our exploratory findings, we argue that future research should investigate interventions that are more directly integrated into the search process, as well as such that combine boosting IH with encouraging searchers to approach the search task in an IH-driven way and promoting transparency for appropriate reliance on the search system and ranking.@en