Advanced modeling is a challenging endeavor and good tool support is of paramount importance to ensure that the modeling objectives are met through the efficient execution of tasks. Tools for advanced modeling should not just support basic task modeling functionality such as easy-to-use interfaces for model creation, but also advanced task functionality such as consistency checks and analysis queries. Enterprise Architecture (EA) is concerned with the alignment of all aspects of an organization. Modeling plays a crucial role in EA and the matching of the correct tool to enable task execution is vital for enterprises engaged with EA. Enterprise Architecture Management (EAM) reflects recent trends that elevate EA toward a strategic management function within organizations. Tool support for EAM would necessarily include the execution of additional and often implicit advanced modeling tasks that support EAM capabilities. In this paper we report on a study that used the Task-Technology Fit (TTF) theory to investigate the extent to which basic and advanced task execution for EAM is supported by technology. We found that four of the six TTF factors fully supported and one partially supported EAM task execution. One factor was inconclusive. This study provided a insight into investigating tool support for EAM related task execution to achieve strategic EAM goals.