Dispersal kernels are the standard method for describing and predicting the relationship between dispersal strength and distance. Statistically-fitted dispersal kernels allow observations of a limited number of dispersal events to be extrapolated across a wider landscape, and form the basis of a wide range of theories and methods in ecology, evolution and conservation. Genetic parentage data are an increasingly common source of dispersal information, particularly for species where dispersal is difficult to observe directly. It is now routinely applied to coral reef fish, whose larvae disperse over many kilometers and are too small to follow directly. However, it is not straightforward to estimate dispersal kernels from parentage data, and existing methods each have substantial limitations. Here we develop and proof a new statistical estimator for fitting dispersal kernels to parentage data, applying it to simulated and empirical datasets of reef fish parentage. The method incorporates a series of factors omitted in previous methods: the partial sampling of adults and juveniles on sampled reefs; the existence of unassigned dispersers from unsampled reefs; and post-settlement processes (e.g., density dependent mortality) that follow dispersal but precede parentage sampling. Power analyses indicate that the highest levels of sampling currently used for reef fishes is sufficient to fit accurate dispersal kernels. Sampling is best distributed equally between adults and juveniles, and over more than ten populations. Importantly, we show that accounting for unsampled or unassigned individuals - including adult individuals on partially-sampled and unsampled patches - is essential for a precise and unbiased estimate of dispersal.