Galaxy clusters are excellent cosmological probes provided that their formation and evolution within the large-scale environment are precisely understood. Therefore, studies with simulated galaxy clusters have flourished. However, detailed comparisons between simulated and observed clusters and their population – the galaxies – are complicated by the diversity of clusters and their surrounding environment. An original way initiated by Bertschinger as early as 1987, to legitimize the one-to-one comparison exercise down to the details, is to produce simulations constrained to resemble the cluster under study within its large-scale environment. Subsequently, several methods have emerged to produce simulations that look like the local Universe. This paper highlights one of these methods and its essential steps to get simulations that not only resemble the local large-scale structure but also that host the local clusters. It includes a new modelling of the radial peculiar velocity uncertainties to remove the observed correlation between the decreases of the simulated cluster masses and of the amount of data used as constraints with the distance from us. This method has the particularity to use solely radial peculiar velocities as constraints: no additional density constraints are required to get local cluster simulacra. The new resulting simulations host dark matter haloes that match the most prominent local clusters such as Coma. Zoom-in simulations of the latter and of a volume larger than the 30 h^−1 Mpc radius inner sphere become now possible to study local clusters and their effects. Mapping the local Sunyaev–Zel’dovich and Sachs–Wolfe effects can follow.