Question: Are there any world-wide known Music Certification tests that you can take to use in your resume: for example, to demonstrate basic musical abilities?

I used to work in IT, where it is very common for companies like Oracle and Zend to arrange that kind of certification for a programming language or framework.

Answer: 
Adding to @danmcb answer: In some cases a college degree matters. E.g. in some countries Master in music is required to teach in a public school. A degree might be a plus when applying for other music related jobs.

But if the focus the job is music performance, a video showing you playing will be worth more than any paper. A degree is for sure worth mentioning, but bragging about it too much might actually make a bad impression.

Anything below academic level probably won't be worth much, except when you apply to study at the college.
**Nothing completely world-wide, it seems.**

I'm just a hobby musician, but before joining this stack I had never heard of the type of "grades" people seem to use to measure proficiency with musical instruments. I live in **Sweden**, and it doesn't seem to be a thing here. There are entry exams you need to pass to get into music schools and academies, of course, and there is collaboration between universities to standardise some tests, but nothing as organised as what I see people discuss here, and certainly not for children.

Just to be sure, I asked my girlfriend. Her parents are both professional musicians, and she's been playing the violin in various organised contexts since she was a kid. She majored in music in high school, continued at [Folkhögskola](https://en.wikipedia.org/wiki/Folk_high_school#Sweden)(no idea how to translate..) and then spent 5 years at [university](https://en.wikipedia.org/wiki/H%C3%B6gskolan_f%C3%B6r_scen_och_musik) to become a music teacher. A teacher should know about this, if anyone. She had never heard of anything remotely like the "grades" either.

**There might be something that's fairly global, I don't know, but at least in one country it's not a thing.**