Dispersal kernels are a standard method for describing and predicting the relationship between dispersal strength and distance. 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 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, where larvae disperse over many kilometers and are too small to follow directly. However, it is not straight forward to estimate dispersal kernels from parentage data, and while a number of different methods have been published, these have been examined systematically, and each has substantial limitations. Here we develop and test a new statistical estimator for fitting dispersal kernels to parentage data. The method incorporates a series of factors omitted in previous methods: the partial sampling of adults and juveniles on sampled reefs; accounting for 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 an area of less than twice the mean dispersal distance (particularly when sampling is limited). Unlike previous methods, accounting for unsampled adults - both on partially-sampled and unsampled patches - is essential for a precise and unbiased estimate of dispersal.