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I have. Double wrapped and in a ziplock bag... You then thaw it and slowly heat it back up in the oven. It is not so good in the microwave. Be sure to pour the juices in with it. Never a problem for me...
The tenderloin will not be as tender and it will be good. I second elzabethintexas in that you cover it with the juices or some kind of liquid before you freeze it or it wil be dry. And when you reheat it (not in the microwaves as Elizabeth says) make a some kind of sauce to add over it - a port wine reduction sauce for example.
Cynthia is a trusted source on Bread/Baking.
If you slice it before you reheat it, then as mentioned, reheat it slowly with its pan juices or some stock in a covered baking dish, you'll have a good result and avoid the unpleasant taste and texture you can sometimes get from a re-cooked protein. Reheat, don't re-cook.