Even though the Zachman Framework is a highly referenced framework for enterprise architecture (EA), there is still a lack of adoption by EA practitioners. Some of the factors that contribute towards this lack of adoption is the absence of accepted methodologies for adopting the Zachman Framework as an EA approach, as well as the lack of CASE tools supporting the practical use of the framework. In this paper we present the results of an investigation into methodological support when using UML together with the Zachman Framework for EA modeling. From this methodological study, we established evaluation criteria for tools that claim to support the Zachman Framework. We furthermore used these criteria to evaluate three popular CASE tools that claim to support the Zachman Framework. We focus specifically on the evaluation of the CASE tools' ability to assist a modeler with populating the cells of the Zachman Framework according to Zachman's criteria when using UML as a modeling notation.