Something which is easy to say but non-trivial to execute on (I know I have to get better at this and it has quite recently cost me thousands of dollars): do not negotiate against yourself. You'd be surprised -- I've been surprised -- at how high clients can go when they're sufficiently motivated to solve a problem. Their conception of money is totally different than your's or mine. Don't sell yourself short by e.g. assuming that there is a "fair" price which you can't go above. (Mutual agreement makes any price fair.)
It helps to think in terms of selling value instead of hours, though that can be a tricky thing to calculate. But if nothing else you can assume that if some client is willing to pay $insane for your time then they have decided it's at least of that value to them.
Of course, if you have some knowledge that allows you to guesstimate this value then so much the better.
