There is an art to this. These situations come up because you want to continue an ongoing relationship into the future.
So you quote a price that is high, but not so high as to destroy the relationship. I call it "plausibly-deniably-high".
You also have to gauge the context of the other party in the negotiation. This technique works best when you accompany the quote with some kind of description matching the personalities. Some people are swayed by a description of the additional time it takes (the billable hours mentality). Others are swayed by a description of the additional risks you are bearing on their behalf to deliver the outcome. Still others are swayed by a description of the de novo technical challenges that no one else has ever attempted before. The list goes on, and is a fascinating study into people.
This is where a real salesman (as opposed to an order-taker) earns their keep, where they know how to read a room and craft a response, messaging and after-meeting socializing that takes into account all those perspectives simultaneously from the point of view of the other party.
So you quote a price that is high, but not so high as to destroy the relationship. I call it "plausibly-deniably-high".
You also have to gauge the context of the other party in the negotiation. This technique works best when you accompany the quote with some kind of description matching the personalities. Some people are swayed by a description of the additional time it takes (the billable hours mentality). Others are swayed by a description of the additional risks you are bearing on their behalf to deliver the outcome. Still others are swayed by a description of the de novo technical challenges that no one else has ever attempted before. The list goes on, and is a fascinating study into people.
This is where a real salesman (as opposed to an order-taker) earns their keep, where they know how to read a room and craft a response, messaging and after-meeting socializing that takes into account all those perspectives simultaneously from the point of view of the other party.