Academic copy editing is a highly specialized job; it is important not to rush into hiring someone without considering some key factors, which I have set out below.
Hire an academic. Choose an editor who has an employment background in academia and/or a PhD in a relevant area. Hiring a generalist editor is fine for fiction books or websites, but when you’re dealing with scholarly writing, your best bet is to hire someone who specializes in academic copy editing. For example, you wouldn’t hire a family lawyer to deal with a medical negligence case, would you?
Hire someone who offers a free trial edit. It is not fair to expect clients to pay for editing services if they haven’t had the chance to assess the editor’s work first.
Hire an individual editor rather than a company with employees. If you hire a large company, you don’t necessarily know who will be editing your manuscript. The company may claim that all their editors have PhDs, but how do you know this is actually the case? Even with freelance editors, if in doubt, double-check that they are not contracting out the work to someone else.
Do your research. Check that the editor actually provides a name and Google him/her. Believe it or not, there are some companies out there with no named person as owner! It is preferable to choose an editor who has a strong online presence, with a location and a regular phone number displayed on the website; your best bet is to deal with a real person, who is contactable (not a faceless company).
Consider whether prices are realistic. If something is suspiciously low-priced, look elsewhere. For example, if someone is offering to edit your 160 page thesis for $200, you might as well throw your money down the drain; a thesis of that length may take 10 days to edit… no self-respecting scholar can afford to spend 10 days working on a manuscript for $200.
I hope these academic copy editing hiring tips are useful. Good luck in your search!