How can I ensure I have a better magicka regeneration rate during combat?

From this guide: Mage Guide

It seems the best way is to reduce the spell cost, rather than increase the regeneration rate.

Copied from the guide:

Now for the unlimited mana...

1. Find an item that 'reduces the mana cost of destruction spells.
2. Disenchant to learn the "Fortify destruction" spell.
3. Get your enchanting skill up into the 40+ range.
4. Get enchanting perks that make it 20/40/60/80/100 more effective.
5. Get the 'insightful' 'corpus' and 'extra effect' perks as you can.
6. Get your hands on 3 Grand soul gems with Grand souls.
7. Get your hands on a ring, necklace, and circlet you like.
8. Apply the 'fortify destruction' enchant to all three, and equip them.

Yes, there are perks for magicka regeneration (see in restoration at least).

There are also items that increase X% of magicka regeneration.

But the higher the cost of the spell you use, the faster magicka depletes. So try to get the cast for half cost perks too, and eventually, reduce cast cost upgrades on your gear.

Unfortunately it seems that magicka regeneration improvements do not affect your in combat regeneration.

Magicka regeneration out of combat is set to give you 3% of your total magicka per second, but while in combat that drops down to 33% of the normal regeneration rate, meaning only 1 percent of your total magicka is regenerated per second. This does not seem to factor in any magicka regeneration gear when in combat.

Over at Skyrim Nexus they have mod files for adjusting your in combat regeneration. Personally I'd just settle for somehow applying your magicka regeneration gear to the in combat regeneration rate, but that doesn't seem to work unfortunately. I'm sure someone will mod it soon.