You do not.
My stand on that would be simple: you do not ask after the fact. Period. Means: you should have asked BEFORE ORDERING the certification, not now that you got it.
I generally only refund costs that are one of the following:
- Budgeted (which is actually a special case of blanket preapproval).
An exam is neither. As such, if an employee orders this before having a PO accepted - there is NO refund. Never. Out of principle.
Whether the exam HAS happened or not is irrelevant.
Now, for approval: is the exam NEEDED and does it provide additional business value? if not - automatic reject, I am not in the business to spend money on non business relevant expenses. And yes, most computer certifications are not actually NEEDED, legally. There are few exceptions: more for certain consultancies (customer demands it, so it is either have it or not getting work), less in the MS world (certified partner requires a NUMBER of certifications in the company, which can be a lower number than employees, so no automatic approval, and the business value is a bag of goodies worth MORE than maintaining the certifications = business value) but in general: no, pieces of paper.