Stack Overflow currently gives no indication to the setter of a bounty that he will have 24 hours after the deadline to award the bounty. Please add some sort of message, both in the "Bounty Creation Wizard" and also in the Bounty Text that the user can see for the duration of the week.
It seems to me that the "your bounty expires soon" email reminder would be a perfect place for this.
Not sure it makes sense to add it to the creation process...
Once the bounty expires, the bounty banner changes to something like "This question had a bounty worth +X reputation from Y that ended just now; grace period ends in Z", so we could be more clear about what the grace period means there as well.