First, you should watch Amy Cuddy's TED talk on body language and the "power pose":
...if only so you'll know what people are talking about when they reference it, because it'll probably be brought by someone, at some point :) There's a transcript here, if you don't like to watch videos, though you'll probably need to get at least some visuals to go with it to understand what she's talking about, so here's one: \o/ (that's you with your arms raised above your head in a victorious V, more or less)
I don’t know how much those power pose techniques actually help me directly, but in general, getting in some movement to get my blood pumping a bit and psyching myself up helps. As always, do whatever works for you to cheer you up and get pumped, whether that's a power pose and/or a pep talk to yourself in the bathroom mirror. One thing I might try next time is to do some jumping jacks or something, so that I can tell myself that my raised heartrate is not due to fear, but from that exercise.
On that note, this is also a useful TED talk, on how you can re-interpret your physiological responses to stress to your own benefit (and I swear I'm normally not that TED talk fan type, I much prefer reading articles to watching videos):
Anyway, if none of the above works for you, draft some friends to be on call to help! Your friends are probably a better cheerleader for you than you are for yourself.
Remind yourself of your achievable goals, and how you want to express how positively you feel about this offer, and how it’s a collaborative effort to make this opportunity even better on all sides.
And lastly, bring whatever notes you need to remember all the stuff that you've practiced and prepared. I pretty much always also write up a Post-it note as a reminder to myself to SLOW. DOWN. when I’m talking, so that I sound more confident and competent.
Once you wrap up the negotiation itself, remember to end the conversation on a positive note, expressing your excitement about the company. If they ask you what you're feeling right then about the offer (as code for "can you just tell me or give me a hint on whether you're going to accept?"), you can say something like this:
"I'm really excited about this opportunity! I will just need to take some time to consider all* the factors for my decision. Thank you so much for taking the time to discuss all these details with me, it's all been incredibly helpful."*This is basically code from you, for "you could always consider sweetening the pot further and letting me know to help me make this decision in your favor."
Needing to take some time to consider a decision really isn't something that can be reasonably argued against--and if you get pressure to accept very quickly, that is a very bad sign. Either this company culture is tending to be abusive, or the most charitable interpretation, you're working with a recruiter that isn't very good. See this essay from Joel Spolsky on the "exploding offer":
Almost any company, when pressed, will give you a chance to compare offers. Don’t worry about burning bridges or pissing anyone off. Trust me on this one: there’s not a single hiring manager in the world who wants to hire you but would get mad just because you’re considering other offers. It actually works the other way. When they realize you’re in demand, they’ll want you more.Finally, end the conversation by clarifying next steps, like what you or they have agreed to do--they need to get approval from someone else on what you've asked about, they'll send you a revised offer with the new details, you need to get back to them with a final decision by a certain time, etc. This is just to make sure you're all on the same page about what's been agreed to (or not).
I hope you find this series of posts helpful! Please do let me know if it has in fact helped you at any point so I can validate some of my opinions (though you should also let me know if any of this advice is really horrible or seems misguided too, of course). Best of luck!
Update: here's the full series of posts