Gah, can anyone tell me how I am supposed to kill the guardians from the capital cities? I've got my enemies cornered, but I can't crush them once and for all because my troops get demolished by the guardians within the first turn. I really don't want to resort to grinding levels for my characters, because that's really, REALLY slow.

Your not meant to kill them is the thing. The mission or scenario you are on should have some objective that when completed allows you to win. The best thing to do is get a couple lower end heroes and camp the outside of the enemys base. If you wiped out all the enemys heroes already anything that comes out should be at the basic level allowing for a fair fight. Just keep rotating the heroes in and out of gaurd duty whenever they lose troops or are to injured to fight.
It is possible to kill the gaurdians but you need a hero around level 10 with some great gear and a ton of 1day use potions to buff yourself up. You also need some top tier monsters to go along with your hero. The main stat that needs to be increased is your damage reduction(can't remember the name disciples gives it). If you get that up to I think its 90% on your hero and enough of your men you might beable to survive long enough to kill the gaurdian.

Ahhh. That makes sense. Thanks for the help! Next time I'll read all my mission objectives more thoroughly.

As has been said, in most scenarios you're not meant to be able to take a capital (one exception is the final Clans mission in the Gallean's Return expansion). In Disciples 1 taking a capital is very, very hard, even with maxed out units and 90% armor; you still typically need a mass healer to mop up the damage you take, as even little bits will add up over a long battle (and those battles are very long, as in you'll usually end up auto-retreating after 10 rounds and have to attack again to finish it off). In Disciples 2 things become a bit easier because you can get much more powerful units, but 90% armor is still a must, and damage-raising buffs are also highly recommended.

Additionally to raising your armor, you could also try paralyzing the guardian if you have a unit or an item that is capable of doing that. Of course, you still need enough armor (or HP) to survive the first attack...
Also quite neat to know is that "spcial damage" (e.g. the frostbite of Sons of Ymir, or poison) bypasses the armor of the guardian. Which is the sole reason why I keep an assassin around if I play the Humans.

I did not try the higher difficulty levels, however on "easy" they are most certainly not.
I made extensive use of petrify (Legion's "Incubus" unit) and paralyze (through the "Soul Crystal" in the human campaign), and killed lots of Guadians during my playthrough.

Interesting. I played all my games on normal difficulty, so it looks like the guardian's vulnerability changes significantly between difficulty levels.

The main thing is you need to get max armor to survive the initial blast. High hitpoints helps too, but armor helps more. Best of all worlds is to get both. Getting the skill "natural armor" helps a lot on this for your leader, as it adds 20% armor. That can sometimes help you spare a potion for the other members of your group. It also argues for even the offense oriented evil sides holding onto a defense artifact, at least until level 15 when the appeal of killing guardians diminishes because their experience isn't needed anymore.
I'm not sure what the dwarf equivalent is to the other sides' ability to fight the guardian. But you can start killing guardians at fairly low levels with the right line-up of skills, items, or team members. Basically you need to paralyze the Guardian. Or whatever each side wants to call it.
Empire -- Soul Crystal (artifact, level 4 I think)
Legions -- Incubus, to petrify (level 4 again I think)
Undead -- One of your warrior choices has the paralyzing skill. So does the ghost/spectre/shade, but it doesn't stick reliably enough to kill a guardian.
I don't know if at any point it becomes available, but any side that gets a soul crystal can paralyze. And as my mage found out, it does paralyze multiples.
Guardians can give a couple thousand in experience, so it is well worth it to try them. You can gain (your level x 2) + 1 more level per "level" or whatever of the game itself, and the game becomes more fun when you do, so it's well worth the tediousness of the guardian battle to try to kill him. Doing so also sometimes gives you the spells, mana, and coin held by that faction, which is especially good for the undead and legion, whose spells for the most part cannot buff or heal them and therefore for the most part cannot even be used to fight towns, guardians, or anything not outdoors.

The other day I killed a guardian on the 3rd level, if I remember correctly, I was playing with The Mountain Clans. As others mentioned previously, you need to get your armor up. Collect/buy as many potions of protection/invulerability as you can. With an armor value of 90, the 250 damage attack of a guardian only does 25 (plus a little) damage. With the elf unit Theurgist - which has an awesome attack BTW -, it became a theoretical possibility to lower the armor of the guardian with the Theurgist's attack Shatter. I guess the developers thought of this too, since in Rise of the Elves, the guardians have immunity to Shatter. What a shame! :-)
Regards,
Vorax