This part is the story of how I did this repair badly and then went back and did it right. My initial plan was to just cut off the boards that were rotted and replace them with new boards.
The flaw in this plan is that tongue and groove is typically installed so that no two boards end at the same place, so having a section of boards all the same length was really conspicuous.
The other flaw in this plan is that modern tongue and groove is not the same width nor thickness as the tongue and groove that was installed on my porch in 1953 when they built the house. So not only did the boards look odd because they all ended at one spot, they also had some awkward gaps to try to make up the difference in width.