When does my employer coverage actually end? - 14 months and counting

I was told my coverage ends on my last day, but the letter says the end of the month. I am in Oklahoma City, in case local advice matters. I do not want to be surprised by a bill. What should I do about appointments?

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.