The design and maintenance of large computational science systems can be aided greatly by the use of generic computational science libraries. The object-oriented design of software using a generic library presents many advantages over non-object-oriented or non-generic based software design. However, the testing of generic libraries involves some unique issues not usually faced during the testing of non-generic libraries. This paper will describe these testing issues as they pertain to libraries designed using C++ templates. A proposed solution to these issues using a usage model-based automated testing framework will be presented.