You tell them that due to the competitive nature of both of the businesses, they should "make an offer based on competitive intelligence and public information".

I cannot find a good link on it, but I think Novell used this technique when being approached by Microsoft.

My understanding is that this is what a breakup fee is for. If they back out, at least they're paying for it.

You don't.

I'll suggest that if your competitive advantage is something so easy to lose that somebody following you around your office for a day could break your business, maybe you should reconsider your business model.

This is even more true for "tech" companies...if you hinge on people not knowing how your special sauce works, you've probably cocked up the business side of things pretty badly.