in all negotiations, like your salary, it's always better to let the other party give the first shot. Never give in to saying your price first. You should have a rough range in your head, though, on what's payed in practice, but usually ranges are very wide on what prices are payed for a certain thing, or service.
If the other party is aware of a common pay range, they will probably tell you the bottom of the range. That's when you can address again the value of what you will provide (in the end, you already know they want what you have, otherwise they would have looked further), and tell them to think again (still not saying your price, but you can let shine through that their first offer really wasn't adequate. Far from it). Give them time to think about it again. Probability is, that the next price they say is near the upper end of the range. And as i said, the range, depending on what is negotiated, can vary greatly. Good luck.
Cheers,
Frank