The hard part is to get the client on the phone.
Once you have them on the phone, you can not only better understand their problem but also demonstrate your skill and credibility in a way no resume or branding could.
At that point it's just a sales game - generally you'd avoid hourly rates and sell them a solution (see my other comment) which will maximize your effective hourly rate while being structured in a way that's very good value for the client. Hourly should be a last resort, at which point generally you'd rather have the client bounce, so you quote a high rate.
That last part is exactly why I charge $999/hour.
I'll offer a specific solution that takes me a week of full time work (14 hours each day -- I'm focused) for about $10k, which is roughly $150/hour if you want to calculate it that way, or another specific solution that takes me 3 weeks of 10 hour days for $15k which amounts to $100/hour. And like any good consultant, I'll eat the cost if I'm wrong. Other times I'll charge $40k when I know it will take a few months of dedicated work and I have to really lock in.
In practice, I never actually charge hourly. So the $999/hour is really Schrodinger's rate.