Passive microrheology is an experimental technique for the characterization of complex polymeric fluids based on the tracking of small embedded colloidal particles which undergo Brownian motion. Key modeling features for this flow problem include viscoelasticity of the suspending medium as well as the possibility to incorporate thermal fluctuations consistently. In this article some numerical methods suitable for the simulation of passive microrheology are reviewed. The so-called micro-macro approaches are based on the coupling between the continuum hydrodynamics description of the complex liquid with microscopic simulations of polymers using Brownian Dynamics. The advantage of using these methods is related to the consistent incorporation of thermal noise as well as the possibility to simulate microscopic polymer dynamics exactly. On the other hand, computational limitations are mainly due to the fact that in order to reproduce realistic conditions a large number of stochastic realizations is generally necessary. An alternative approach that bypasses the use of micro-macro models is represented by a Lagrangian particle method based on Smoothed Particle Hydrodynamics. In this method the viscoelasticity of the solvent is modelled via a continuum Oldroyd- B model whereas thermal fluctuations, inherently present at the microscopic scale, are incorporated into the particle framework by application of the GENERIC formalism, ensuring the strict fulfilment of the Fluctuation-Dissipation theorem. As an application, the particle method is used to simulate a realistic case in passive microrheology. In particular, a rigid structure suspended in the viscoelastic solvent is modeled and the rheological properties of the Oldroyd-B fluid, namely frequency-dependent storage and loss moduli, are extracted through the standard microrheological route, that is, by measuring the probe mean square displacement (MSD) and linking it to the solvent viscoelasticity by assuming the validity of a generalized Stokes-Einstein relation (GSER). Good agreement with the analytical theory for the Oldroyd-B model is observed only up to maximal frequencies corresponding to time scales considerably larger than the Brownian time of the probe particle where the diffusive regime is fully established. At larger investigated frequencies, a crossover between diffusive and ballistic behavior for the MSD of the probe is observed and validity of the GSER is questionable. The model presented here provides an optimal computational framework to complement experimental observations and to analyze quantitatively the basic assumptions involved in the theory of microrheology.