1. There is always flexibility in the budget for the right people.
I'm hiring engineers to my team right now and I have a clear number I got from my CEO. I am confident that budget will fit the ideal candidate that I'm trying to hire. But on the other hand, if someone more senior, or junior blows my mind, I'm willing to push for the extra numbers for the more senior, or the extra rack for the junior to get on my team.
2. Salary is not everything.
I do believe salary is important, but not everything. There are a good number of people who are willing to take a job with less salary if they feel they can grow there more, the culture fits them better and the potential of company is bigger there.
I do understand though it is frustrating doing multiple interviews without knowing if the salary range is close to the expectations or not. If a candidate asks me on the initial phone screening about the numbers I am happy to talk about it openly.