Reason I'm asking is because I recently started freelancing in software/web development (about 6 months ago) and I think I'm doing okay. I love to design and think out all of the odd, interesting or difficult back-end problems and so far all of my clients love my work, and with that I'm slowly increasing my rate, started at 50eu/h ($55/hr) and am currently at 75eu/h ($82). This is all in Europe (The Netherlands) However I feel like I'm a bit stuck, the clients I'm able to find don't want to pay more then $80 and with that the work isn't as challenging as I'd like it to be. At the same time it feels like the clients that do want to pay more aren't looking for me.
To make it easier to charge more you have to go after customers who are less price sensitive, whose problems are costing them a lot of money, and who are accustom to acquiring outside help for things outside what they consider to be their core business & expertise.
In my case this was big enterprises. Nationwide law firms, banking & fin. tech. institutions, international distribution & logistics companies, etc.
It took a long time to build up to that point and to get access to those parts of the market. The way it worked for me was, early-on, I'd be doing smaller jobs for big companies. Sometimes with another vendor as an intermediary. So, I might work with Boeing or Lockheed indirectly, but I was fastidious about establishing direct personal relationships. Once I hit the media & marketing world, it was the same pattern. Work through an existing vendor of say Pepsi or Nike, and then make direct personal relationships that could grow later for their adjacent or orthogonal needs.
Eventually you have enough contacts and enough of a reputation that you don't need to leverage the credibility of intermediaries anymore.
I don't know that such a path would work for everyone for all kinds of work (everything I ever did was kind of esoteric for its time), but that's what worked for me.
$350/hr+ was distributed database related consulting, and then started going North from there for increasingly niche and specialized consulting services. Though only on very rare occasion these days. The highest rate I've ever been able to negotiate was $1,000/hr. But, it was also for a very short engagement (~10 hours) for some especially weird knowledge I have about replacing critical mainframe infrastructure with commodity systems.
Point being, you might be surprised how much you can charge for the right services to the right customers who have a clear sense of need and appropriately value a solution.