Okay well I'm predominantly a Dwarf player, so I'll do my best here. First thing's first, go to www.bugmansbrewery.com/forum and check out their School of Battle. They have a thread on VC, a thread on necromancy and a thread on death magic which will all be useful. If your opponent is a brewery member then he will be well versed in tactics, so good luck ;)
Dwarven elite units can all have banners up to 50 points in cost. It is a very common thing for units to take a rune of Stoicism (double unit strength) or a rune of courage (immune to fear and terror), indeed many people take them in their all comers lists, so you should assume they have them, especially if they know they face the undead.
These runes plus the ld 9 of Dwarves mean you can't rely on fear as much as you do against the weak elgi or grobi (but you knew that ;)).
the tried and tested method of simply using wights for damage and zombies to remove ranks is a great one. Zombies are weak and will never acomplish much alone, but Dwarves don't do much damage, so they wont be gaining much CR by killing the zombies. The denied ranks, flank bonus and outnumber will often see you achieve the all important auto break.
However with this in mind your opponent will be using his artillary to thin your units and his excellent anti magic to prevent buffing them back up. The banner of doom is usually considered expensive for what you get, but against dwarves your GG will really like it.
Bolt throwers, grudge throwers and cannons can all have runes on them, any rune no matter what the primary effect, will make the WMs shots magical, so don't assume your ethereals are safe.
The shooting of the Dwarves will really ruin your day if you let it. You MUST get into combat quickly. As soon as your DW leave cover the organ gun will eat them. use Danse Macabre, book of arkhan, cover, banner of doom, anything you can to protect your primary, non fodder units. If you are going to attack his WM then do so with a lot of units at once so he can't shoot them all, or danse them into combat. Summoning bloodlines can be good here, but you have to be careful.
If a unit of hammerers has a lord in it, then it is immune to fear and terror.
Banshies are somewhat useless. with the Dwarven ld 9, banshies must roll an 8+ to score any kills at all, and with WS 3 + S3 they are going to have trouble wounding anything with CC.
All that's left to say is that Dwarves are rock hard, don't ever feel like it might be a good idea to fight them one on one. There are many runic combinations that will ruin a vamps day, and the basic warrior is more than a match for any non wight unit. Be selective.
P.S. There is a thread here that deals with teh anvil of doom. check it out if you are likely to face one.