A good hiring manager will know the upper limits of what they are willing to pay and, at the same time, keep that information to themselves. After all, they have a budget and it's there job to spend that money in the best way possible.
Your job is to determine the minimum amount of money you are willing to work for. When the manager asks how much you want then you need to say so. So, make sure you quote them a price above that minimum so that you have room to negotiate.
When delivering this amount do so with full confidence that you are worth every single penny; believe me, it helps.
If that amount is either near what they are willing to pay or under it then the manager will likely counter. If the counter works, accept it. If it's below your minimum then let them know that you can't go below $x. At this point a good manager will likely stop the conversation saying they need to get approval (whether they actually do or not).
Some managers may just accept your price right there. That doesn't necessarily mean you "left money on the table" so to speak. It might just be how they work.
Point is: know what you want and don't be afraid to ask for it. It might take a negotiating a few times to get there but as long as you aren't too far out of line then you'll get it. Further, what they are willing to pay shouldn't impact your happiness at what you are willing to work for.