The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.