Fastest-path queries between two points in a very large road map is an increasingly important primitive in modern transportation and navigation systems, thus very efficient computation of these paths is critical for system performance and throughput. We present a novel method to compute an effective admissible heuristic for the fastest-path travel time between two points on a road map, which can be used to significantly accelerate the classical A∗ algorithm when computing fastest paths. Our basic method-called the Hierarchical Separator Heuristic (HSH)-is based on a hierarchical set of linear separators of the map represented by a binary tree, where all the separators are parallel lines in a specific direction. A preprocessing step computes a short vector of values per road junction based on the separator tree, which is then stored with the map and used to efficiently compute the heuristic at the online query stage. We demonstrate experimentally that this method scales well to any map size, providing a high-quality heuristic, thus very efficient A∗ search, for fastest-path queries between points at all distances-especially small and medium range. We show how to significantly improve the basic HSH method by combining separator hierarchies in multiple directions and by partitioning the linear separators. Experimental results on real-world road maps show that HSH achieves accuracy above 95% in estimating the true travel time between two junctions at the price of storing approximately 25 values per junction.