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Honestly I've never had a problem challenging the PCs in combat.  Should every combat be kill-em all?  No.  Should some of the combats be "kill-em all"?  Sure.  You should have the ability to threaten an Epic level PC's hit points.  Now, by that time they should be really invested in a whole ton of other stuff you can threaten, but the card should be on the table.

Epic Level enemies should be unfair.  Epic level enemies should use paragon level enemies like terrain (and they should function like terrain similar to their counterparts.  If you are fighting the lord of the dead while jumping on the heads of his amassed undead horde, it should feel like it.  The key isn't challenging the PCs at a certain level (honestly, take exp budget and throw it out the window.  Just make sure you keep it somewhere in the level of reasonable for your party), it should be making the encounter not last 10 years.  Yeah a party of 5 could take 20 at-level standards, but that would take forever.

Here is what I do for epic level combat:
1) Preroll trivial things in the encounter.  Or completely make up different things that might be a roll and have a sheet of numbers in front of you that you are crossing out.

2) Simplify: In the above example the zombie horde "terrain" does damage and other effects.  Roll a d6 and use that for if the player is effected by the "terrain enemy".  Figure out what the defense that terrain is attacking and order the PCs from lowest defense to highest defense (keep it on a side sheet nearby).  At Terrain initiative and when the player triggers it roll a d6.  If that PC is that number of lower they get effected.  So if the terrain "attacks" reflexes then the person who has the lowest reflex is going to get constantly hit by those effects (he only gets missed on a 1) and the highest person will only have a 1/6 chance of being hit.  Have it do static or prerolled damage and effects.  Avoid save-ends as it can clutter the field if you are using an army they are wading through.

3) Simplify: Everything in the encounter should do the same dice.  No exceptions.

4) Be unfair, but fairly: Use mechanics like "when effected by X you take double damage from all sources."  Let them know the triggers and how to avoid them.  Weaken and the double damage effect are your friend.  Avoid using weaken or insubstantial too terribly much, but keep it on the list.

5) Stop player turns: The best epic monsters won't be chained from full health to dead in a flurry of blows.  All of your elites should function like mini-solos and be able to push/pull/slide/teleport/daze/cripple your multiattackers should they hope to survive.  Your solos should be able to banish players into an extra diminsional pocket for a turn for causing them problems.

6) Attack their resources liberally.  Epic level "minion" fights should steal healing surges on a regular basis, sometimes two at a time.

7) Once death is not a true kill, introduce them to stuff that will completely kill them no-questions asked if they fall victim to a particular attack.

8) Steal mechanics from anything you can:  Especially from games that require a lot of timing and/or teamwork.  One of my monsters was stolen directly from Brutallus and did extreme damage in a blast in front of him.  The damage increased by 1 increment for every PC not caught in the blast area.  So with 5 PCs he was doing x4 damage to the one PC.  If you have these mechanics they should either be survivable, researchable or they should have lesser versions on the littles before they face Big Bad.

9) Incapacitate the Leader: The leader should be the engine for your party.  Sometimes the best thing an enemy controller can do to your party is remove the leader from the fight for a round.

10) Don't include Lurkers in your budget:  Include them in the powers of the creatures.  Epic enemies should be able to summon forces, create primordial shadows or literally call down the heavens on you.  Being able to summon low health high damaging monsters can really hurt a group if they leave anything alive after the alpha strike.

11) Shield your minions: Make your minions take 3 hits.  A hit of X threshold counts as 2 hits, a hit of X*3 counts as a one shot.  At epic level this should roughly be your level.  So a minion takes 3 hits of anything, 1 hit of 21-60 and one other hit or a single hit of 60 or more.

12) Fight in Waves:  Again people can summon minions from anywhere, don't have the encounters be single things most of the time.  Have them be part of a world where portals in and out of combat can be common.

Edit - Clarified some things and:
13) Every now and again, after you have set the bar, lower it a bit.  Your players should still have the ability to turn some baddies into red mist and walk through an encounter.  You are epic, if you aren't fighting a climactic epic battle, no need to be stopped doing everything. -Compliments Fardiz