As only females contribute directly to population growth, sexual females investing equally in sons and daughters experience a two-fold cost relative to asexuals producing only daughters. Typically, researchers have focused on benefits of sex that can counter this ‘cost of males’ and thus explain its predominance. Here, we instead ask whether asexuals might also pay a cost of males by quantifying the rate of son production in 45 experimental populations (‘lineages’) founded by obligately asexual female Potamopyrgus antipodarum. This New Zealand snail is a powerful model for studying sex because phenotypically similar sexual and asexual forms often coexist, allowing direct comparisons between sexuals and asexuals. After 2 years of culture, 23 of the 45 lineages had produced males, demonstrating that asexual P. antipodarum can make sons. We used maximum-likelihood analysis of a model of male production in which only some lineages can produce males to estimate that ~50% of lineages have the ability to produce males and that ~5% of the offspring of male-producing lineages are male. Lineages producing males in the first year of the experiment were more likely to make males in the second, suggesting that some asexual lineages might pay a cost of males relative to other asexual lineages. Finally, we used a simple deterministic model of population dynamics to evaluate how male production affects the rate of invasion of an asexual lineage into a sexual population, and found that the estimated rate of male production by asexual P. antipodarum is too low to influence invasion dynamics.