Genitalia are among the most studied phenotypes because they exhibit high anatomical diversity, experience fast evolutionary rates and may be shaped by several evolutionary mechanisms. A key element to uncover the mechanisms behind such impressive diversity is their copulatory function. This topic has been overlooked, especially concerning structures not directly involved in sperm transfer and reception. Here, we conduct a hypothesis-driven experimental study to elucidate the operation of various external genital parts in five species of stink bugs with differing levels of phylogenetic relatedness. These insects are unique because their male and female genitalia are externally well developed, rigid and composed of multiple components. In contrast with their anatomical complexity and diversity, we show that genital structures work jointly to perform a single function of mechanical stabilization during copula. However, distinct lineages have evolved alternative strategies to clasp different parts of the opposite sex. In spite of a high functional correspondence between male and female traits, the overall pattern of our data does not clearly support an intersexual coevolutionary scenario. We propose that the extraordinary male genital diversity in the family is probably a result of a process of natural selection enhancing morphological accommodation, but we consider alternative mechanisms.