The first thing to consider is planning. It is recommended that you keep at least a week's supply of any consumables you will need for your pets in or near your emergency shelter. You should plan in an emergency how you plan to deal with your pets. You should also realize that during an emergency you pet is likely going to be acting differently than they will during normal calm periods. If you have an animal that is normally caged taking them out of the cage then you will want to make sure you have a transport carrier or cage ready that the animal can be safely kept in.
If you have more than one pet, make sure that everyone knows what to do with each of your pets during an emergency and set up who has the primary responsibility for each animal. Doing this will help get the animals to safety rather than trying to figure out what animals still need to be rescued.
Finally as sad as it is to lose a pet your life is much more valuable than that of your pet. Do not put yourself at great risk to save your pet. Running into a burning building to look for a loose pet is a lost bet. If the animal was loose it may already have escaped and run away. If it is trapped inside unless you know right where it is chances are more likely you will be injured than you will be able to save your pet. Tell the firefighters where the pet is, if they can save it they will.
Recently an area about 10 miles from my home lost over 1000 homes to an F4 tornado. The local vet clinics have been offering a weeks free boarding for animals to help their families get a chance to get on their feet. This is pretty common, as a friend of mine had the vet offer them the same when they lost their house to a fire. So I would recommend you call your vet and see if they can help, or if they can refer you to someone who can help.
There are also some families offering to foster animals until the families are back in a position to care for their animals. This is a risk but if you are unable to afford to board your animals for the months it may take to rebuild, this may be an option. I expect most of the people offering this service are doing so in good faith. But I would still want to vet them before I turned over any of my animals.
This is also something you can plan for. Talk with your family and friends and see if there is someone willing to commit to helping you out with your pets should the need arise. This is also something to think about in case you need someone to take care of your animals should you and your family become unable to. We have an arrangement for our dogs with one friend, and our rabbits with another. So if something were to happen we know they would be taken care of.