How to deal with language evolution

So I've got these two countries who speak the language, because ones a colony of the other. The thing is that these countries have been seperated for around five hundred years. One country hasn't had any communication with anyone but themselves, while the other has had multiple countries interact with it. How do the languages differ? I want someone from one country to be able to community with another, but how would they sound to another? And more importantly, how do I get it to be obvious in dialogue without becoming clunky? While I could make one sound old timey, say Shakespearean, does that keep when the perspective shifts? Is it present in narration? Should I just avoid making any changes and just have it sound to the reader the same language?