ABSTRACT We present a post-processing catalogue of globular clusters (GCs) for the 39 most massive groups and clusters in the TNG50 simulation of the IlllustrisTNG project (virial masses $M_{200} =[5\times 10^{12} \rm {\!-\!} 2 \times 10^{14}$] M⊙). We tag GC particles to all galaxies with stellar mass M* ≥ 5 × 106 M⊙, and we calibrate their masses to reproduce the observed power-law relation between GC mass and halo mass for galaxies with M200 ≥ 1011 M⊙ (corresponding to M* ∼ 109 M⊙). Here, we explore whether an extrapolation of this MGC–M200 relation to lower mass dwarfs is consistent with current observations. We find a good agreement between our predicted number and specific frequency of GCs in dwarfs with $\rm {\it M}_*=[5 \times 10^6 \rm {\!-\!} 10^9]$ M⊙ and observations. Moreover, we predict a steep decline in the GC occupation fraction for dwarfs with M* < 109 M⊙ that agrees well with current observational constraints. This declining occupation fraction is due to a combination of tidal stripping in all dwarfs plus a stochastic sampling of the GC mass function for dwarfs with M* < 107.5 M⊙. Our simulations also reproduce available constraints on the abundance of intracluster GCs in Virgo and Centaurus A. These successes provide support to the hypothesis that the MGC–M200 relation holds, albeit with more scatter, all the way down to the regime of classical dwarf spheroidals in these environments. Our GC catalogues are publicly available as part of the IllustrisTNG data release.