I didn't send a signed message because I don't know how to do it in a Ledger device via Ledger Manager (I don't feel safe using the old Ledger Wallet Bitcoin chrome app). Also, it seems it doesn't support it. Plus the fact the I also doesn't think my PC is not safe enough to expose the private key and enter to an Electrum install.
Use: File -> New\Restore -> Standard Wallet -> Use a hardware device
And then follow the instructions. Once the wallet is successfully created, you can use the "Tools -> Sign/Verify Message" option to sign a message using the address of your choice from the Ledger device.
I've tested this just now with a Ledger Nano S and it works fine.