While I understand that it is not customary or typical to acquire website links though the Twitter platform, it is quite possible - however probable to expect.
What methods or techniques might be used to encourage a website link? Is there anything?
Simply searching for a type of account tagline, like "Editor at some site"? Even then, are they apt to make the transfer, from Twitter to posting a link on their own site page? Seems the driving reason/motivation behind it would have to be a strong one.
Twitter is a contact too so the same rules apply that you'd use in any other communication... Build a relationship, have value.
You're not going to get much in the way of quality results just tweeting out a generic request to every editor / manager / operator you can find.