Lots of authors I know have a hard time finding an editor because they feel that they want to “know” their editor. This is understandable when you’re entering into a developmental relationship, but copyediting and proofreading are much more technical skills. The best copyeditors and proofreaders I know are freelancers who are hard to find because they’re working for publishing houses, and the only people who have access to them are companies and/or individuals with stables of editors they’ve cultivated over years in the industry. If you find a service (or individual) you trust with access to a stable of editors, be open to being assigned to one. Ask about the individual’s qualifications, and what other books they’ve edited, but let the trial edit be the deciding factor rather than any connection you hoped to have between yourself and your editor.
Another online editing service is Scribendi, which has over 300 experienced and educated editors. They've been around a long time. With this service, you decide how fast you want the book edited and how extensive the edit should be, then they match you with an editor. You don't ever actually meet the editor, but rather work through their customer service team. Their prices depend on your requested turnaround time and word count. You can get a free quote here.
Blake, that’s wonderful info. Thank you. I completely understand the response about guaranteeing the work. That was just something that popped in my head as I read a book written by a screenplay consultant I hired years ago and he wanted a review so I read it to help him out but found maybe 5 or 6 error’s myself in the 200 page book. I felt like it was unprofessional but didn’t have the heart to tell him. But the errors stuck out like a sore thumb so I was curious if that is normal or not.
A site where you can hire editors on a freelance basis. Has a range of prices so there is something to suit most budgets. Be sure to take the usual caution when working with a freelancer. Check out their reputation carefully first and communicate carefully with them in order to determine a schedule, payment expectations, methods of communication etc.
Recently a client asked me to do a sample edit and quote to copyedit his MS, which is a biography of his late grandfather’s career (and exploits) as a senior police officer early last century. When I did a short sample edit (4 pages), I realised there were some pretty major issues with his writing and the structure. So I sent it back with my comments and we discussed doing an MA, which I did. Now he’s working on sections of his MS and then sending them to me (he has poor health so we are doing it in stages). It’s a collaborative effort and we’re enjoying working on it together. If you have a client who is open to working with their editor, their book can become something they are really proud of, and it’s equally satisfying for the editor.
When you get that email, particularly if it's your first book, make sure you are well-rested and in a positive frame of mind before you open it. If it’s your first book, the editing process will be hard on your ego, but remember, the editor’s job is to make your book better and help you learn the craft. You are paying for them to give you critical feedback, not to pat you on the back and say ‘good job.'

I’d add that for UK writers, the Society for Editors and Proofreaders (SfEP) Directory is the best place to search for editorial professionals. Each editor has been vetted for professional competence through the Society (you have to be assessed to become a Professional Member or Advanced Professional Member), so it’s a pretty trustworthy source: http://www.sfep.org.uk/directory/directory.asp

2. Copyeditors aren’t the last line of defense when it comes to a book’s mistakes. Formatting, which is done after an editor has done their job, can lead to unintended errors being introduced into the text. That’s why it’s important to hire proofreaders to comb through edited text *after* the book has been formatted for print or digital. Proofreaders are your last line of defense—but they’re human too.
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