We present a constrained reverse Monte Carlo method for structural modeling of porous carbons. As in the original reverse Monte Carlo method, the procedure is to stochastically change the atomic positions of a system of carbon atoms to minimize the differences between the simulated and the experimental pair correlation functions. However, applying the original reverse Monte Carlo method without further constraints yields nonunique structures for carbons, due to the presence of strong three-body forces. In this respect, the uniqueness theorem of statistical mechanics provides a helpful guide to the design of reverse Monte Carlo methods that give reliable structures. In our method, we constrain the bond angle distribution and the average carbon coordination number to describe the three-body correlations. Using this procedure, we have constructed structural models of two highly disordered porous carbons prepared by pyrolysis of saccharose at two different temperatures. The resulting pair correlation functions are in excellent agreement with those obtained by diffraction experiments. Simulated transmission electron microscopy (TEM) images of the resulting models are compared to experimental images. Many of the features observed in the experimental images are also observed in the simulations. The model carbons are characterized by determination of the porosity, pore size distribution, adsorbent-adsorbate potential energy distribution and adsorption properties at zero coverage, using a model of nitrogen as the adsorbate. Grand canonical Monte Carlo simulations of nitrogen adsorption in the model materials are presented and it is found that the results can be explained in terms of the adsorbent-adsorbate potential energy distribution but not in terms of the pore size distribution. For both models, the isosteric heat of adsorption is a decreasing function of coverage, in agreement with typical experimental results in other porous carbons.