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1.
The term used when you call someone and they hit the ignore button on their cell phone, to avoid speaking with you.

The term originates with Nextels because they have a side button to do that.

You know you've been side buttoned if it rings for a shorter time than usual before going to voicemail.
Mark: Oh no! Greg is calling
Jessica: Don't answer it!
Mark: Good idea, I'll side button him.

Greg: What the fuck, TWO rings? Fuck Mark for side buttoning me.
de Li Hibbs 21 août 2005
 
2.
The action of ignoring an incoming call by the use of the side button on one's cellular phone.
"Dude, I totally side buttoned this chick last night. She must have called me five times."

de Taylor H. 2 mars 2008