An apparatus and method for estimating a parameter of a lithographic process and an apparatus and method for determining a relationship between a measure of quality of an estimate of a parameter of a lithographic process are provided. In the apparatus for estimating the parameter a processor is configured to determine a quality of the estimate of the parameter relating to the tested substrate based on a measure of feature asymmetry in the at least first features of the tested substrate and further based on a relationship determined for a plurality of corresponding at least first features of at least one further substrate representative of the tested substrate, the relationship being between a measure of quality of an estimate of the parameter relating to the at least one further substrate and a measure of feature asymmetry in the corresponding first features.