2. Wait and See
If a valuable tree appears to be a borderline case, resist the temptation to simply cut it down and be done with it. In such cases, it may be best to stand back for a while and think it over. Remember that time is on your side. After careful pruning of broken branches, give the tree some time to recover. A final decision can be made later.
Examples:
On the Fence
A mature shade tree can usually survive the loss of one major limb. Prune the broken branch back to the trunk. In the months to follow, monitor large wounds closely for signs of decay. Learn how to repair and prevent future damage
Easy Does It
Resist the temptation to prune too heavily. Remember, the tree will need all the foliage it can produce to make it through the next growing season. Remove only the damaged limbs—wait and see what happens. Learn how to repair and prevent future damage
Hold Off
A healthy mature tree can recover even when several major limbs are damaged. With large trees, bring in a professional arborist 
to assess damage on a borderline situation and to safely accomplish needed pruning and branch removal.
Don't Try to Do It All Alone
Some of your trees may have damage that's too close to call, or may have hidden damage. You may need a tree professional to help you decide what to do. Don't hire just anyone who shows up at your door following a storm. Look for qualified arborists or contact your city forester.