Have you tried using Bluetooth? It doesn't necessarily matter if either phone is native to Vzw, but rather will they communicate properly if you decide to use the Bluetooth method to transfer your contacts.
Are they both BlackBerry devices? You can back up the old BB using Desktop Software (free download from the BlackBerry site), then activate the new BB and use Device Switcher to move everything over. I believe you can use BB Desktop Software to transfer contacts from other types of phones, too, but I've never tried it.
Congrats on your new Verizon post rrowley! Your peers had some great suggestions between Blackberry Desktop Manager and bluetooth. To give you any other suggestions, I'd need to know what make/model phone you're going from and to. That way I can give you the best method possible if you haven't already made the transfer yourself.
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The easiest method is to sync all contacts with Gmail. This will reload your contacts to any phone that you load Gmail on to. You don't even have to use the Gmail account...just create it to sync contacts. Works for calendar events also.