Hi DelDance,
Sorry for the delay in reply! I always hope that others will join in the discussion, so I tend to wait just a bit before I chime in.
The way we teach it, it's actually not necessary to raise the hands much at all, though there is some very minimal room to shift the hands upward for those who find it helpful. However, care must be taken not to raise the hands too high, because there's an inverse relationship between room above the follower's head and room between her head and the whole of her arm. In other words, in trying to give the follower more room under your hand, you give her much less room between her head and arm. So much so that in fact I personally teach the leader to circle the hand as close above the follower's head as possible (short of actually touching her head) in order to maximize the space everywhere else.
More problematic than the uncomfortable appearance of lack of space caused by a hand held too high, is that it also diminishes the couple's ability to lead and follow. The higher you hold the hand, the longer the connection and smaller the circle, meaning the information transmitted through that connection becomes increasingly subtle. The most effective connection, then, is one where the follower can maintain some bend and tone in the arm, and the circumference of that circle is maximized to make it more obvious the direction and speed of the circle.
A common misconception is that the follower should turn under her own arm and hand. This misconception causes interesting problems for inexperienced dancers. Newer leaders tend to draw a circle that is not far enough around the follower's head, forcing the follower into either a contorted arm or a contorted body position to accommodate. Her hand should always be able to remain more or less directly in front of her face throughout the duration of the turn, even at the moment she is facing directly away from the leader.
On the flip side, inexperienced followers will tend to contort themselves without much help, even if the leader is doing his part. This is due in large part to preconceived notions of underarm turns, such as imagining that the follower's arm should be raised, that she turns under her own arm, or that the lead is indicated by simply raising the hand. I generally have student followers work on holding the arm in a static position with the elbow bent, upper arm aimed straight ahead and forearm aimed straight upward, palm forward, staring at the back of the hand. This allows me as leader to move the hand in any direction, including in a full circle to the left or right, and trust that they will always follow the direction and speed I'm leading.
So to answer your question specifically: How high do you raise the hand? To her it should either feel like nothing at all, or as you mentioned, a tiny bit to her forehead level at absolute most. And even that much isn't required. To you as leader, it will feel like quite a bit more stretch, but that has less to do with how much you raise the hand as how much you reach to get the hand all the way around her head. There's also more variation in the leader's elbow position and upper arm angle than the follower's, which is especially important at the onset of an underarm turn to left (leader's forarm nearly parallel to floor). I could get into a lot more detail, but that's the baseline of it.
I hope that helps! Feel free to continue the discussion if this raises more quetions.
Regards,
Jonathan Atkinson