Sex-biased dispersal is well known for birds and mammals, typically by females and males, respectively. Little is known about general patterns of sex-biased dispersal in other animal taxa. We reviewed return rates for a model group of invertebrates (damselflies) and explored putative costs and benefits of dispersal by males and females. We used published capture–mark–recapture data and examined whether a sex bias existed in likelihood of recapture at least once, at both emergence and/or breeding sites. We assessed whether this metric of likelihood of recapture was indicative of dispersal or philopatry, and whether any emerging pattern(s) were consistent across damselfly families. Using a meta-analysis, we found a higher likelihood of recapture at least once for males than for females at both natal sites and breeding sites, which seemed attributable to higher female-biased dispersal, although female-biased mortality cannot be discounted particularly for some species. Sex biases in dispersal among damselflies may be understood based on sex differences in maturation rate and foraging behaviour, both of which should affect the costs and benefits of dispersing. This hypothesis may be useful for explaining patterns of dispersal in other animal taxa.