Does CodeWarrior IDE support software debugging of MCF51JM128?
This should be obvious by the MCF51JM128 home page. Click on "tools &amp; software". 

Scroll down to "IDE - Debug, Compile and Build Tools" where it lists Codewarrior for MCU. For free, you'll only get the crappy Eclipse debugger though. Useful debuggers will cost money.

However, I would strongly recommend to avoid Codewarrior for MCU, it is an utterly horrible tool chain. Throughout my career I have used at least 50+ different tool chains and this one is by far the worst I have ever encountered, all categories. Everything in the IDE is simply broken.

If you have an older PC you can use the much better Codewarrior Classic 6.3. Unfortunately, NXP has blocked it from use in Windows 7/10 but it can be installed through hacks.

Similarly, LPCxpresso is quite awful too. So unless you can find &amp; afford a good 3rd party tool chain, I would stay clear of NXP products.