Abstract: Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. The talk presents progress on computing the self-force in a gauge that is constructed from the gauge-invariant Weyl tensor. The gauge and the renormalization method are chosen to compute a perturbed metric and renormalized self-force from the Teukolsky equation. The method is related to earlier work by Cohen, Kegeles, Lousto, Detweiler, and Whiting, and to the MiSaTaQuWa renormalization. Work by Keidl and collaborators suggests an appropriate gauge and finds a closed form solution in that gauge for static charges and masses in a Schwarzschild background.