SmallRig Cage for HERO13 BlackWorth buying only for the use it is built around. The only one on this page recording Cold shoe mounts — 2; Material — Aluminum alloy. Not for you if this matters: Not waterproof; use it for impact protection and accessory mounting.
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Which of these protective housings also fit another device
Fit rarely carries across generations, so this lists only the exact models each product is separately documented to fit.
What looks like it fits GoPro HERO13 Black but does not
Lens mods and ND filters sold for HERO9 through HERO12 are the common wrong buy: HB-Series is a different mount.
These sit in the same protective housings aisle and are confirmed for a different exact model. We have no published answer saying any of them fits GoPro HERO13 Black, so treat them as unverified for this device rather than as a fit.
FitStill 60 m Waterproof Housing for HERO9 BlackConfirmed for GoPro HERO9 Black. Not confirmed for GoPro HERO13 Black.
FitStill Double-Lock Waterproof Housing for HERO5 BlackConfirmed for GoPro HERO5 Black. Not confirmed for GoPro HERO13 Black.
FitStill Waterproof Housing for HERO8 BlackConfirmed for GoPro HERO8 Black. Not confirmed for GoPro HERO13 Black.
GoPro HD HERO2 Replacement Waterproof HousingConfirmed for GoPro HD HERO2. Not confirmed for GoPro HERO13 Black.
GoPro Protective Case for MAX2Confirmed for GoPro MAX2. Not confirmed for GoPro HERO13 Black.
Coming from an older model
Why a previous-generation protective housing may fail here
HERO13 Black introduced the HB-Series lens system and a magnetic latch mount in place of the older folding-finger mount.
Enduro batteries and the general mount ecosystem carry across from HERO12, but lens mods and filters made for earlier HERO generations do not attach.