  We present a systematic construction of the Penrose coordinates and plane
wave limits of spacetimes for which both the null Hamilton-Jacobi and geodesic
equations separate. The method is illustrated for the Kerr-NUT-(A)dS
four-dimensional black holes. The plane wave limits of the near horizon
geometry of the extreme Kerr black hole are also explored. All near horizon
geometries of extreme black holes with a Killing horizon admit Minkowski
spacetime as a plane wave limit.
