Question: I see that, for example:

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> A cleric or paladin can use a holy symbol as a spellcasting focus, as described in chapter 10. To use the symbol in this way, the caster must hold it in hand, **wear it visibly,** or bear it on a shield.
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Further, I see that the standard arcane focuses -- orbs, crystals, rods, etc. -- all have to be held in the hand. That makes sense to me.

What I'm *not* sure about is, for example, the *Hat of Wizardry* or the *Dark Shard Amulet* from XGTE. Both specify they can be used as a spellcasting focus (for wizards and warlocks respectively), but it does not make sense to me that e.g. a wizard would be required to hold their *Hat of Wizardry* in their hand to use it as a spellcasting focus, instead of wearing it. I can imagine a warlock having to grip their *Dark Shard Amulet* with a free hand, but that still seems like a bit of a stretch, especially when combined with somatic components.

Can these specific foci be used without holding them in hand?

Answer: 
The *[Hat of Wizardry](https://www.dndbeyond.com/magic-items/hat-of-wizardry)* says:

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> This antiquated, cone-shaped hat is adorned with gold crescent moons and stars. While you are wearing it, you gain the following benefits:
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> * You can use the hat as a spellcasting focus for your wizard spells.
> * You can try to cast a cantrip that you don’t know. [...]
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The text seems pretty clear to me - while you're wearing it, you can use it as a focus. Holy symbols for clerics and paladins work the same way (they only need to be worn, not held), so it is not unprecedented. It has a specific verbiage that overrides the general rules.

Furthermore, it seems relatively well balanced: It consumes a precious attunement slot and only works for wizard spells. If the character is multi-classed, they'll still need a different focus, even for classes that can use a more general arcane focus. Sure, it has a second property, but it's only once per long rest.

The [Dark Shard Amulet](https://www.dndbeyond.com/magic-items/dark-shard-amulet) has functionally similar text, except aimed at warlocks.
**Yes**, the *Hat of Wizardry* and the *Dark Shard Amulet* must be held in hand to be used as focus.

The rule for material components is found in the Player Handbook's errata:

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> **Material (M)** A spellcaster must have a hand free to access a spell’s material components—or to hold a spellcasting focus — but it can be the same hand that he or she uses to perform somatic components.
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This makes it clear that a free hand is required to hold the spellcasting focus.

For the Holy Symbol, its description (p. 151) specifically states that it can be used as a spellcasting focus under broader conditions than normally allowed by the rules:

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> **Holy Symbol**. A cleric or paladin can use a holy symbol as a spellcasting focus, as described in chapter 10. To use the symbol in this way, the caster must hold it in hand, wear it visibly, or bear it on a shield.
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However, there is no such mention in the description of the *Hat of Wizardry* and the *Dark Shard Amulet*. The text only states that they can be used a a focus:

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> **Hat of Wizardry**. You can use the hat as a spellcasting focus for your wizard spells.
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> **Dark Shard Amulet**. You can use the amulet as a spellcasting focus for your warlock spells.
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This is not different than the description for other foci, such as the Arcane Focus:

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> **Arcane Focus**. A sorcerer, warlock, or w izard can use such an item as a spellcasting focus, as described in chapter 10.
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The only difference is that the hat and amulet have the additional requirement that they be worn before they can be used a focus.