A resume is good for providing a chain of trust to prove that you have a certain set of skills. You say you have skills x, y, and z, and you prove that you have these skills by saying you did A, B, and C and some company, and contacts at that company can if need be verify that you did these things. At the beginning of your career, this rests on your education and transcript to show you've taken a certain set of classes and done well in them and therefore are likely to possess the required skills.
As a hobbyist, you don't really have this chain. You only have what you've built. The best thing you can do is have really excellent documentation of what you've done. Pictures, plots, explanations, a coherent story behind your projects. If you interview and your projects are small enough, you might bring one in your backpack or something.
You might have a "personal projects" section on your CV. "Designed narrowband varactor-tunable microwave VCO with XX dBc phase noise at 10 KHz offset" or whatever, and next to it a (hopefully short) URL that links to a page which documents how you measured and achieved such performance, or alternatively a youtube video that documents the design decisions and your measurements, mistakes, and how you recovered. Make the documentation comprehensive enough that there's no doubt that you built such a thing and achieved such-and-such level of performance.
Indeed all this is easy for software developers... you just link to your github. Then you can just read the code, test it, look at the quality, etc. This is why so many programmers come from hobbyist backgrounds. It's very easy to verify a person's skill. For EE it's harder. What you have are schematics, data, layouts, etc. If an interviewer goes through there and your work all adds up to the final product you claim, you're golden.