I post this on twitter:

Then, one hour later I get this message from Twitter:

from Twitter
subject Six Apart is now following you on Twitter!

Hi, eirikso.
Six Apart (sixapart) is now following your updates on Twitter.
Check out Six Apart’s profile here:
http://twitter.com/sixapart
You may follow Six Apart as well by clicking on the “follow” button.

Best,
Twitter

Sixapart makes Movable Type. The biggest WordPress competitor.

Look for people talking about your brand on the internet and follow them! But you should also follow people that talk about your competitor.