Until recently, the estimation of the heritability of a trait has required knowledge of the pedigree within a population. In natural populations such knowledge is often unknown. Two techniques have been developed which use marker information to estimate heritabilities without reference to the exact nature of the relationships: a regression-based estimator that regresses phenotypic similarity for a pair of individuals against an estimate of their relationship and a likelihood-based estimator that maximizes the probability of the genotypic and phenotypic data given a known population structure. Computer simulation was used to compare the behaviour of these estimators. Bias in estimates of heritability decreased with increasing marker information, decreasing simulated heritability, increasing relatedness and increasing sample size. The techniques displayed reasonable tolerance to the percentage of missing data. The regression-based technique shows least average bias, but largest variance over simulations. Likelihood-based techniques show larger average bias, but smaller variances over estimates. A modified form of the likelihood technique, requiring fewer initial assumptions about population parameters, is presented. The modified form shows less bias in its estimates of heritability than the likelihood technique originally proposed.