I know you can't give a TO to the team without the ball while the ball is live. But what if a TO is requested and the ref blows the whistle when he/she shouldn't have? What should you do?

Grant the TO but kick yourself?
No TO, inadvertent whistle, give ball back to offense?

The timeout must be granted.

NFHS Casebook 2004-05 5.8.3 Situation E: The official erroneously grants Team B a time-out in a situation when Team B cannot have one. What happens now? Ruling: Team B is entitled to use the time-out since it was granted. The time-out once granted cannot be revoked and is charged to Team B. All privelages and rights permitted during a charged time-out are available to both teams.

(From my physical book, not my dumb online one. ;) :D)

I think the common sense thing to do is to consider the erroneous timeout as an inadvertant whistle. That does not apply to every situation, but I think for most situations that is the best thing to do.

Peace

Rut is exactly correct that it is an inadvertant whistle. The official blew his whistle when he shouldn't have done so. The problem is that once the whistle blows, the ball is dead. And since either team can request a TO when the ball is dead, if the coach requests the TO again, you have to grant it.