We propose two general and robust methods for enriching resources annotated in the Frame Semantic paradigm with syntactic dependency graphs, which can provide useful additional information for applications such as semantic role labeling methods. One method incorporates information of a dependency parser, while the other one assumes the resource to be based on a treebank and uses dependency graphs converted from phrase structure trees. Coverage and accuracy of the methods are evaluated on the English FrameNet and German SALSA corpora. It is shown that large proportions of those resources can be accurately enriched by mapping their annotations onto dependency graphs. Failures to do so are found to be largely due to parser errors and can therefore be seen as an indicator of incorrect parses, which helps to improve parse selection. The remaining failures are analyzed and an outlook on ways of improving the results by adaptation to specific resources is given.