What employers look for when they want someone with "excellent communication skills" has little to do with anything that would appear on a test unless you are talking about a position that requires writing official documents like documentation, press releases, etc. For an engineering position, "good communications skills" means that you can clearly describe what you are doing, what you intend to do, and what you did, and that when you have a conversation, no one leaves the room confused as to what was agreed to.
I have known plenty of people who were great communicators despite being mediocre English speakers. I have also known plenty of completely fluent people who were horrible communicators. "Communications skills" doesn't mean you can find the best synonym to "dyspeptic". It means that you understand what others mean, and can clearly express your ideas.
Though to be honest, when I see "good communications skills" on a resume, I ignore it because everybody says that. How true that is usually comes out in the interview anyway.
Now if your applying for a position as a copyeditor, maybe it is different.