The standard lightning impulse voltage wave used in transformer factory testing does not properly cover all the overvoltage stresses that a transformer can experience while in service. To properly asses the internal overvoltages that can occur in practice, we propose to interface the manufacturer's white-box transformer model with EMTP-type simulation tools using a black-box modeling approach. From the white-box model we compute in the frequency domain data for the blackbox model which are fitted with rational functions, including voltage transfer functions from external terminals to internal nodes. The resulting black-box model is easily interfaced with EMTP-type circuit solvers via a Norton equivalent and recursive convolution. Application to the so-called fictitious transformer used by CIGRE A2/C4.39 demonstrates that ground fault initiation on a connected cable can generate internal overvoltages that exceed those of the lightning impulse test.