Will a ham sandwich pass through TSA?

Since you've already traveled I will state an answer anyways. Checked baggage or carry-on is fine. (See below.) Solid foods poses no problem. If brought as carry-on, just keep it stowed in your carry-on baggage when submitting it through x-ray.

From http://www.tsa.gov/ ("Can I Bring My.." search tool.)

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Search Results For: sandwich

Check or Carry-on

Solid food items (not liquids or gels) can be transported in either your carry-on or checked baggage. Liquid or gel food items larger than 3.4 oz are not permitted in carry-on baggage and should be placed in your checked baggage if possible.

All food products should be properly packaged to avoid spilling during the screening process and damaging security equipment and other passengers' belongings. Cakes and pies are permitted as carry-on items, but could require additional screening.

Even if an item is generally permitted, it may be subject to additional screening or not allowed through the checkpoint if it triggers an alarm during the screening process, appears to have been tampered with, or poses other security concerns. The final decision rests with TSA on whether to allow any items on the plane.

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Not a problem. I have often take sandwiches from home when I travel.

I doubt it, you would be surprised how many ham sandwiches are sneaking through airport security.

Unless the TSA eats it, you are good to go. I hope yours is on rye, with swiss cheese, and grain mustard.

You'll probably be fine. If they complain, just eat it.

You are fine