I found stock certificates for Disney and Sony that were given to me in 2011

Neither Sony nor Disney stock has split since 2011, so the value of each is still 1 share. The current value of 1 share of Sony stock is about $103, and 1 share of Disney stock is $174.

While that's nothing to sneeze at, it's not a life changing amount either. I think the novelty of having a physical stock certificate for such popular companies is worth more than the actual face value of the stock. As far as I know you can't purchase real stock certificates from either company anymore (though Disney does offer personalized proof-of-ownership certificates for entertainment purposes).

If they were mine I would consider framing them. They should always theoretically be worth at least as much as a share of stock, and will likely grow in novelty value over time. (Though if someone buys it with intent of cashing it in, the value would potentially be lower due to transaction fees.)

Make sure to photograph them in case they are ever lost or stolen and you need to re-issue, re-register, or sell in the future.

First of all, you should have been receiving dividend checks from both Disney and Sony all these years. If you haven't, it probably means that they don't have your current address. The dividends themselves are going to be too small to even worry about for only one share, but you still need to make sure that these companies know who you are and have your current address.

To register a shareholder account with Disney, go to: https://disney.computershare.com/ When you set up your account, you can choose to have your dividend reinvested into partial shares, so you don't have to deal with a tiny check mailed to you anymore.

I don't know exactly what you need to do for Sony, but their Investor Relations website is at: https://www.sony.net/SonyInfo/IR/

The fact that you have an actual Disney stock certificate is kind of special: They no longer issue new stock certificates. The best thing to do is to keep them and not sell them, unless you really need some cash.

If you do decide to sell, then as Bob Baerker's answer mentioned, the normal way to sell stock that you have a certificate for is to contact a broker and give them your stock certificate. They will put your share in their account for you, and then you can sell it very easily on the market. However, the broker might charge a significant fee for transferring the certificate.

An article from Zacks mentions some other possibilities for selling your stock. You could try selling your shares directly to the transfer agent (Computershare for Disney, Citibank for Sony). Alternatively, you can sell your share to someone else by simply signing the stock certificate over to them.