In terms of shields, you are not able to Elden Ring Runes use your shield when two-handing a weapon in Elden Ring. This is to ensure that you can inflict more damage using both hands on the weapon. Two-handing also makes you more agile since you won't be carrying two heavy armaments at the same time (assuming you use the shield or another weapon in tandem).
If you are sneaking around, we strongly recommend that you two-hand your weapon because the shield is not an issue when it comes to these types of situations. There are also certain boss fights that are more manageable when you use two hands on a weapon particularly when you are able to learn how to deflect attacks instead of defending yourself with your shield. Below is a short video that shows the damage that can be dealt when two-handing the Dismounter greatsword. The initial attack deals the victim 275 damages.
The video below showing the same weapon motion, however, it's being used two-handed rather than one. As you can see, you're much more effective when you're two-handing, specifically dealing 304 damages. It's not a huge difference however, if you're not using your shield anyway then you could be able to take on more damage. It's not necessary to always use two-hand weapons but. Certain scenarios require a shield or a parry counter, while others feature difficult attacks to cheap Elden Ring Items roll through. Try out different strategies and find out the best strategy for any specific enemy. For example the Red Wolf of Radagon boss is possible to defeat without the use of any shield, so you should two-hand in the fight.