Matrilineal systems in sub-Saharan Africa tend to co-occur with horticulture and are rare among pastoralists, with the causal arrow pointing from the introduction of cattle to the loss of matriliny. However, most work on this topic stems from either phylogenetic analyses or historical data. To better understand the shift from matrilineal to patrilineal inheritance that occurred among Bantu populations after the adoption of pastoralism, data from societies that are currently in transition are needed. Himba pastoralists, who practice 'double descent', may represent one such society. Using multi-generational ethnography and structured survey data, we describe current norms and preferences about inheritance, as well as associated norms related to female autonomy. We find that preferences for patrilineal inheritance are strong, despite the current practice of matrilineal cattle inheritance. We also find that a preference for patriliny predicts greater acceptance of norm violating behaviour favouring sons over nephews. Finally, we show that there are important generational differences in how men view women's autonomy, which are probably attributable to both changing norms about inheritance and exposure to majority-culture views on women's roles. Our data shed light on how systemic change like the shifts in descent reckoning that occurred during the Bantu expansion can occur. This article is part of the theme issue 'The evolution of female-biased kinship in humans and other mammals'.