Ghostbusters?
GMs, remember that someone with Connection 6 is not going to be Lofwyr, Damien Knight, Richard Villiers, or Buttercup -- or even Miles Lanier or Roger Soaring-Owl. For those, you should need to purchase things normally restricted to group contacts -- Matrix access, magical access, even numbers to indicate how many people can jump when they blow the whistle. What you should especially hit them up on is the 'Area of Influence'; +4 (National Level) at least, +6 (Global) if they're wanting to snag a real mover and shaker. So if they want Lofwyr as a close personal friend who'd do anything for them, make them wind up spending at LEAST 33 points for him -- if not more, all things considered.
My personal house mod to the contact game has the cost being (Connection ^ 1.25) * (Loyalty ^ 1.1). A Connection/Loyalty 6/1 Friend for Life dock worker will cost you 7 points (+1 for going from 5 to 6), but a Connection/Loyalty 1/6 Just Biz major mob boss is going to cost you 9, because of his reach and influence. A 6/6 Friend for Life mob boss will be a 63-point sink for you -- but on the other hand, this is the guy you can go to for almost anything and probably get it.
I'd also make sure the characters get some amount of free contacts -- Charisma times the highest of Negotiation or Etiquette, perhaps, with a minimum of their Charisma unless they've been Burned. The elven face character (CHA 7, Negotiation 5) will be able to afford 35 points worth of contacts -- a Connection/Loyalty 4/3 contact and a couple of 4/2 contacts, perhaps -- while even a troll thug will get a point or two break.