Besides all the great advice already given in this thread, at high levels I'd alter the game rules slightly - in combat in particular.
Think of a dragon's sweeping tail or the bashing club of a mighty giant - just the size of these creatures means they are not going to miss. So bring back the touch attack (10 + dex + magical bonuses..etc) and let the armour's contribution to AC be usable to offset damage. So that chain shirt does nothing for your AC against these attacks, but is able to soak 3 damage. Have cover do the same - with pillars, furniture, walls lending soak damage but not adding to the AC as the attacks smash away the architecture converting the surrounding terrain into difficult terrain with all the debri or the building becomes unstable.
Things get rather tense if the monster's attack is too big to miss every round and the location becomes an obstacle course.
Have ghosts, spectres and the like ignore physical armours as their ever chilling necrotic touch easily bypasses the breastplate and clothing burying into the character's chest.
Invite degrees of success for Legendary Beasts - so a 10 above the target required converts the hit into critical damage. Perhaps add an effect with every hit (save vs condition - prone, stunned, swallowed, or being pushed/shoved, disarmed etc).
And if failing a spell saving throw by 10 or more, have the damage double - so that the Big Bad Evil Avatar unleashes Legendary Magic which would otherwise obliterate weaker adventurers.
Have Lich's spells cause life-draining damage in an aura around it in addition to the spell's effects instantly slaying familiars or a Demon that saps magic as it casts, so it disables protective spells (like Shield, Mage Armour...etc), buffs (Invisibility, Haste...etc) and other (Waterbreathing..etc) and temporarily even the magic of items worn or carried wane for a round as the spell is cast.
Give beasts a Might trait, where each size the beast is greater than the character, it gains an additional +4 bonus to the beast's strength based checks. That should make characters think twice about grappling anyone or anything.
Turn a dragon's breath weapon x 100 - imagine what it does to weapons, clothing and armour and your backpack. Leave the hit point damage the same, but potion vials carried explode, clothing and gear becomes irreparably damaged, fires carry on burning, acid leaves pits, cold and heat attacks affect weapons and armour, making it unbearable to hold a weapon or wear any metal, think adding affects such as Heat/Freeze Metal in certain dragon attacks for those captured in the blast. Have the bow strings melt away. It does a lot to enhance the danger and lengthen the duration of combat if SS and GWM are unavailble for a round or two because the weapons are damaged or too hot or cold to be carried.
And please give monster's threatening reach, especially as the character's are trying to scramble away to safety, pick up a weapon knocked 15 feet away or head towards the nearest body of water screaming "It burns, it burns, my God it burns!"
These and other simple ways to interpret the battle that ensues can make even high-level characters feel humbled by it all.
Lastly and most importantly, don't forget as DM, you need to smile as this is all going on, as it is a game at the end of the day and it shouldn't be taken seriously.