A crucial component of major transitions theory is that after the transition, adaptation occurs primarily at the level of the new, higher-level unit. For collective-level adaptations to occur, though, collective-level traits must be heritable. Since collective-level traits are functions of lower-level traits, collective-level heritability is related to particle-level heritability. However, the nature of this relationship has rarely been explored in the context of major transitions. We examine relationships between particle-level heritability and collective-level heritability for several functions that express collective-level traits in terms of particle-level traits. When this relationship is linear, the heritability of a collective-level trait is never less than that of the corresponding particle-level trait and is higher under most conditions. For more complicated functions, collective-level heritability is higher under most conditions, but can be lower when the function relating particle to cell-level traits is sensitive to small fluctuations in the state of the particles within the collective. Rather than being an impediment to major transitions, we show that collective-level heritability superior to that of the lower-level units can often arise 'for free', simply as a byproduct of collective formation.