As far as money is concerned, old antennas are not worth much more than the little that you might get to recycle them. Simply put, not many people are in the market for old antennas. If your antenna is made from aluminum you may get a couple of dollars at your recycling center. 

Keep in mind that most antennas are top-heavy. If you are on a ladder be prepared to brace yourself when you dismount it. Tools to have handy before climbing up are wrenches, pliers, a lubricant, and a hacksaw. Be prepared for dealing with rusted fittings. 

The price to remove an antenna all depends on what type of antenna and how difficult it will be to get to and dismount the antenna. If removing an antenna on a roof expect to pay at least $100 for the removal service. 

You may want to recycle your TV antenna at your local recycling center or landfill to receive a very small profit. Or you could list it for a small price or free on an online social media community site. Maybe repurpose it as a garden trellis or other creative piece.  

If you are looking to remove a TV antenna keep in mind that professionals who remove old satellite dishes often also remove TV antennas. Many people enlist the help of professionals because removing a TV antenna from a rooftop can be a dangerous task.