Why do I get an “Error 501/505 - Not implemented or not supported” in JMeter?

This is most likely because the JMeter recording proxy does not support the https protocol. If it’s a screen you can live without, you can just stop/start the proxy recorder around that page (I use the Firefox plugin called FoxyProxy to quickly switch between different proxy configurations).

However, if it is vital to your script (for example, a login page) then you can use an alternative recording tool called Badboy Software. I frequently use this to record HTTPS then export the test plan to JMeter. Alternatively you can manually create the HTTPS request sample yourself.

JMeter can run HTTPS request samplers, it just can’t record them using the native proxy recorder.