Q: "Sorry, we can't proceed without this information." If you're a highly-competitive candidate with multiple offers, that's fine, you can ignore this company or convince them to give you an offer anyway—but if you're the sort of person who would be strongly hurt by revealing your old salary, that doesn't help you because you're also probably less competitive, at least on paper. So this very response exacerbates the gap.
Alternatively, Q (aside): "She's pretty abrasive, should we really hire her?" There are studies that this sort of self-confidence is often perceived as a positive attribute in men and a negative attribute in women.
My most uncomfortable interview experience (nearly 20 years ago) came about because of this problem.
I was working in a job I enjoyed, but that didn't pay well. The money had started to become a problem and I started looking for something better-paid. (This was London in 1997 -- I was being paid about £25K and I hoped for more like £35K.)
I used a recruiter, I told them my current salary and what I hoped to get, and they got me a promising-looking interview.
Cut to the interview, and one of the first questions they ask is "Why do you think we should pay you ten grand more than you're getting at the moment?"
Hindsight gives me many ways to answer this, but at the time I just sat there with my mouth open. I had no idea the agent had told them my current salary, so I was completely unprepared. I was dimly aware that a proper answer would express something about my value to the company, so I couldn't just say "I need more money". I eventually muttered something about that seeming to be roughly the market rate, and the interview was effectively over.
Ask a friend to pay you $1 for contract work that takes you half a minute. Draft a contract if you have to. There, now you are "allowed" to say you've been paid $120/hour.
Just tell them what you would like to get. If pressed super hard, give confusing answers in the same way companies give you. Like total compensation, if you add days off, perks etc.
Or you can use the anchoring effect mentioned in the article to your advantage.
Q: 'What's your current salary?'
A: 'I can't disclose my current salary, but I'd be looking for something around $1.5x to come on board.' where x is your preferred salary.
It's not wrong if you want to save on salaries of your staff. I suspect that the people that answer with a $ number rather than the way you did, are less likely to assert themselves and thus consistently take lower salaries.
Alternatively, Q (aside): "She's pretty abrasive, should we really hire her?" There are studies that this sort of self-confidence is often perceived as a positive attribute in men and a negative attribute in women.