Your dogs are just suffering from nervous anxiety due to the storm. Anything can upset a dog's environment and cause anxiety which will make it pant.
Some easy and natural things you can do is soak a dog biscuit in Chamomile tea and give them that. It will calm the dog, reduce anxiety and may help little Fido sleep.
Lemon Balm is also a good natural relaxer.
If the dog is severely stressful and needs a sedative as well as anxiety relief than I would recommend an herbal solution such as Lemon Balm or Skullcap.
Bach flower treatment is highly popular right now but so is eating flowers in our salads so take that for what it is worth. Meaning all of the above are certainly easy and safe solutions, some are just more viable than the others.
I have actually heard that the thundershirts can be effective as well.
Hope that helps,
FDC