  Gamma-ray bursts (GRBs) comprise of short, bright, energetic flashes of
emission from extragalactic sources followed by a longer afterglow phase of
decreased brightness. Recent discoveries of very-high-energy (VHE, $\gtrsim
100$ GeV) afterglow emission from GRB 180720B and GRB 190829A by H.E.S.S. have
raised questions regarding the emission mechanism responsible. We interpret
these observed late-time emission to be the result of inverse Compton emission
of ultra-relativistic electrons in the GRB blastwave in an external radiation
field, i.e., external Compton (EC), considering both the wind and interstellar
medium scenarios. We present predictions of multiwavelength light curves and
energy spectra, ranging from optical to VHE, and include the synchrotron and
synchrotron self-Compton (SSC) radiation mechanisms as well. We corrected the
EC and SSC model for the $\gamma$-ray attenuation by absorption of photons
through their interaction with the extragalactic background light (EBL). We
compared our results to multiwavelength data and found that EC gives a
satisfactory fit for a given set of fixed model parameters for GRB 180720B,
whereas SSC result in a better fit for GRB 190829A. For both GRBs a wind
environment is preferred over constant density inter-stellar medium, and the
Cosmic Microwave Background as the external radiation field. However, with more
data and an effective optimisation tool we can find a more robust fit of the
model, implying better constraints on the GRB environment and the particle
energy requirements for the emission observed at late times. This has
consequences for future observations of GRBs at these extreme energies.
