If you are wielding a shield, is that arm/hand available to be used to hold another item or object? Or is that arm/hand completely occupied by the shield?
RAW, Your hand is occupied.
The description of a shield in the PHB states...
Shields. A shield is made from wood or metal and is carried in one hand. Wielding a shield increases your Armor Class by 2. You can benefit from only one shield at a time.
Emphasis mine from PHB p144
Thus, the PHB seems to be referring to shields that are 'held' with the hand, not simply 'strapped' to the arm.
In the medieval era, this was the norm. You'd either have a handle you gripped, a handle + a strap, or two straps (but you'd hold one of them in your fist). If you just strap a shield to your arm and don't have it mechanically affixed to your armor or something...the first time something hits it, it's just going to spin, hit you in the face or legs, and then be useless...because there's nothing holding it in place.
So, the back of your shield probably looks like this
or like this
Not by RAW.
A shield is made from wood or metal and is carried in one hand.
Based on this wording, a shield is carried in your hand, which means that you cannot carry another object in your hand.
As a DM making a ruling, I would probably allow some leeway, but the wording is pretty clear.
Yes, of course.
Clearly a character can't use both items at the same time, but holding a small object in the shield hand is easy. Just ask this authentic Viking...
I know the rules don't explicitly state you can, but I don't think that's how 5e was intended to be read or played.
But I'm likely wrong.
Actually if you study combat by Scottish fighters, they held a dagger in the hand with the shield strap while using a basket-hilt sword in the other hand. They performed a 3 tier attack: hit one opponent with the shield and sliced across the opponent's throat/chest with the dagger, punched the next opponent with the basket hilt part of the sword, and then stabbed or sliced a third opponent with the sword blade. So carrying or using a small rod of power in the hand securing the shield is definitely a possibility as shown by the Scots.
Regarding RAW, D&D is a game for social enjoyment, not a set of laws for the purposes of oppression. For my group, if a player comes up with an innovative variation of the game rules that enhances game enjoyment while maintaining game balance, everyone wins.
An example of this is ruling an object can be held and even used by the shield hand but only if it somehow becomes part of the wielded shield (either permanently or temporarily) and the RAW definition of the item allows it to be used "passively". That is, not as a weapon or requiring targeting. For instance, a standard shield can be modified by an appropriate crafter to enhance the shield grip with attachments for a Rod of the Pact Keeper. This would allow the Rod's abilities to be used by a shield-wielding Hexblade warlock.
To provide game balance,
- the attachments must be created and permanently incorporated into the shield by a professional crafter with time and cost required for the work,
- attaching/detaching the Rod to and from the shield requires a full minute not under stress,
- the hand holding the shield/Rod combo grip must not be covered in any way that would interfere with the use of the Rod (as defined by the RAW), and
- dropping or otherwise losing possession of the shield also results in loss of the possession of the attached Rod.
Other requirements can be added, like requiring the shield material to be the same as the Rod, the shield becomes unusable without the Rod as part of the grip, or the shield cannot itself be magical. But my DM wasn't quite that stingy.
It turned out that the shield/Rod combo was useful to the character without throwing off game balance in any way yet it made a simple basic wooden shield that much more precious to the player while draining a bit of the player's funds and allowing the group to make friends with a wood-carving NPC. Everybody won something by way of a simple innovation.