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1.
Noun: Euphemism for a cock-punch.

Origin: Derived from "Who Needs a Good Cock-Punching?" Statshot in the Onion, February 6, 2002, where Bono, of the Dublin band U2, was listed at #1.
Did you hear what Jay said about Dan's new house?

Yeah, he may have earned himself a Belfast Handshake.
by Felix00 June 11, 2009
 
2.
When somebody is in front of you and facing you, grab their shirt and head-butt them as hard as you can. May be followed with an optional smack to their head.
He got a bloddy nose from that Belfast Handshake!

Im gonan give him a good ol' Belfast Handshake next time i see him!
by "Jim" November 22, 2005