A few ideas.
1)
www.salary.com -- learn it, know it, love it. You'll get an idea of a range. Also try looking up whatever the title is (and some variants, e. g. I currently work as a Data Analyst but I also look up Database Analyst and Business Analyst) plus your location, just Google it with the word
salary and see what you get. Also try large companies that might have freelancing jobs, see if you can get a handle on what they pay and then you'll have some real numbers.
2) Don't give a number. This is one strategy. Usually you can get around it with something like
I'd like to reserve this estimate until I know a little more about the position. It's reasonable to request something more. The company will either give you literature (or direct you to it), or tell you to go scratch. If they do the latter, you probably don't want to work for 'em.
3) If you must give a number, give a range. Whatever you were paid at your last job (include benefits and any other perks, if I was to talk about this job, I'd add in commuting costs as I'm paid them here, for example) plus maybe $1k more, up to whatever is reasonably the highest based on whatever you got from doing research. Then you have room to negotiate and it's unlikely you'd be boxed into something very low.
4) A variant on #3 is to average your last three or so similar jobs, or use them as your range if they aren't too different. I know you move around a lot so the numbers are current. But if one of those jobs is from five or more years ago, or from a different economic area, it's really not relevant any more.
If your range is too high, they'll tell you, but you can tell them about your research. And let them explain why it's faulty (e. g.
Conglomco pays more because they're seven times our size! or whatever). If it's too low, they certainly won't tell you.