What methods can I use to prove I own a particular website?
Write in comments in html or write meta author tag in head of page:
<meta name="author"content="Your name ">
If you own the site then you will have access to the hosting and or the code. Hence you can make these edits. But make sure the credentials to site hosting and domain platforms are strong and you are the only person who knows them.
On your about page, add an owner section that has a copy of your public PGP key as a download.
If someone wants you to prove ownership of the site, they can download the public key, then request you to send them a signed a file.
Since they know the public key belongs to who-ever owns the sever, they can infer that person must be you if the public key is able to verify the signature of the file you send them.