This photo shows work we carried out to a 300 years old house almost right next door to the example above. This building had the exact same problem as above.
In this project you will note that the stone shapes are somewhat more random than the first example, and again we have tried to replicate this.
Unfortunately, the client did not have budget to repoint the whole of the elevation, so we tried to match the existing cement based pointing with a colour matched lime mortar. We got it pretty close, and the client and ourselves were both very pleased with the result.