I do project management and recruiting, and I was interested if there were specialized freelance sites for project management and recruiting (especially remote work), just as there are specialized freelance sites for copywriting, for instance.
Does this exist? Is it possible to be a remote freelance recruiter or a remote freelance project manager? How can I go about finding one of these roles, and are there sites dedicated to helping find freelance jobs in these fields?
Possible? Sure. But it you have to consider the nature of project management to understand how to get work.
As the project manager role is so critical to the success of a project, companies seeking this type of person will rely heavily on reputation and familiarity. You may be qualified, but why should a client entrust you with a project if they don't know you or your work? If you're hoping to land a project management gig on freelance.com or some similar site, I think you'll be frustrated.
Start close to home. Identify the companies and management folks you work with on a regular basis. Evaluate your reputation in their eyes. Do they know you as a strong project manager type? If so, you probably wouldn't be posting this question – it would be simple to approach them and indicate your interest in freelancing for them.
On the other hand, you may be known to some extent in your industry, but perhaps your colleagues, clients and vendors don't know you well enough to see you as a project manager. You need to build a portfolio and begin to demonstrate your abilities to colleagues who could become clients.
Express your desire to freelance to business contacts in the course of your regular dealings. "Thanks for the order, Sue. I really enjoy working with your team. Not sure if you know this, but I do some project management on a contract basis, outside of my job here. If can introduce me to anyone in your organization who could use my skills, or if you can recommend me to any of your clients, I would appreciate it."
DANGER: You run the risk of conflicting interests. If you have no intention to leave your employer and only intend to do this on the side, you should be completely forthcoming with your employer. If you intend to create a basis for an eventual leap, you still need to be completely above board, but perhaps less forthcoming. This part is complex and specific to each scenario (ie. post another question with more specifics).
Certainly over here in the UK, there are plenty of opportunities for contract project managers.
Both of the UK's main recruiting sites offer such roles:
(neither offered as a recommendation, and other sites are available)
I am sure that such sites are available in other countries too.
As Andrew has said, in the UK it is common to get contract positions as a project manager but these will generally be for a specific project or set or projects.
To my knowledge it is not that common to freelance as a project manager for lots of companies with lots of ongoing projects.
