ABSTRACT The velocity dispersion of globular clusters (GCs) around ultra-diffuse galaxies (UDGs) in the Virgo cluster spans a wide range, including cases where GC kinematics suggest haloes as massive as (or even more massive than) that of the Milky Way around these faint dwarfs. We analyse the catalogues of GCs derived in post-processing from the TNG50 cosmological simulation to study the GC system kinematics and abundance of simulated UDGs in galaxy groups and clusters. UDGs in this simulation reside exclusively in dwarf-mass haloes with M200 ≲ 1011.2 M⊙. When considering only GCs gravitationally bound to simulated UDGs, we find GCs properties that overlap well with several observational measurements for UDGs. In particular, no bias towards overly massive haloes is inferred from the study of bound GCs, confirming that GCs are good tracers of UDG halo mass. However, we find that contamination by intracluster GCs may, in some cases, substantially increase velocity dispersion estimates when performing projected mock observations of our sample. We caution that targets with less than 10 GC tracers are particularly prone to severe uncertainties. Measuring the stellar kinematics of the host galaxy should help confirm the unusually massive haloes suggested by GC kinematics around some UDGs.