One of the main sources of examples of Einstein metrics has been K¨ahler ge- ometry. Yet we know that several K¨ahler manifolds do not carry K¨ahler-Einstein metrics. It is therefore natural to relax the K¨ahler condition in looking for Einstein metrics. In the 80?s, Derdzi´nski obtained a local construction for 4d conformally K¨ahler, Einstein metrics using extremal K¨ahler metrics. Together with G. Oliveira, we set out to use Derdzi´nski?s methods on a class of extremal K¨ahler metrics arising from an ansatz due to Calabi. In this talk, I shall report on our findings. I will start by reviewing Derdzi´nski?s results and the Calabi anstaz. Then I shall explain how our construction includes Einstein fillings of S3/Zm. I also discuss a cone-angle Einstein deformation of the Page metric on CP2?CP2. If time permits, I shall de- scribe a limiting procedure yielding an asymptotically hyperbolic Einstein metric not arising from the Derdzi´nski construction. This is joint work with G. Oliveira.