Nowadays, a major interest in research activities concerns methods that aim at providing a reliable mean to control and assess the numerical quality of specific quanti- ties, i.e. strict and accurate local error bounds. A general method for robust goal-oriented error estimation relies on the concept of constitutive relation error (CRE), associated to admissible stress fields and classical extraction techniques. This paper first deals with the comparison between different techniques used for constructing admissible stress fields, which are usually required in methods providing for robust global/goal-oriented error estimation. In this work, a new hybrid technique, called the element equilibration + star-patch technique (EESPT), is compared with the two other main existing techniques, namely the element equilibration technique (EET), and the star-patch equilibration tech- nique (SPET) in terms of quality of associated error estimates, computational cost and simplicity of practical implementation into existing finite element codes. Besides, an en- hanced version of the EESPT method has been revisited and demonstrates its relevance to produce sharper estimators. In a second part, we analyze goal-oriented error estimators constructed from the CRE. Two- and three-dimensional numerical experiments are car- ried out to investigate the performance of each estimator for the calculation of guaranteed error bounds on specific quantities of interest.