I know that we need to send individuals HIPAA certificates when they terminate or lose coverage.
If the individual elects COBRA coverage, are we required to provide them with another certificate at the end of their COBRA coverage?

Lynette, yes you are required to send certificates of creditable coverage when a person ceases to be covered under COBRA. See ERISA Section 701(e)(1)(A)(ii) and/or IRC Section 9801(e)(1)(A)(ii).

You could confirm this with your insurance company, but they will only tell you what they think sounds like the answer should be based on roundtable discussions over donuts and coffee. There is a much better chance that you will get the right answer on this message board. (or on the restroom wall)