  While the experimental detection of entanglement provides already quite a
difficult task, experimental quantification of entanglement is even more
challenging, and has not yet been studied thoroughly. In this paper we discuss
several issues concerning bounds on concurrence measurable collectively on
copies of a given quantum state. Firstly, we concentrate on the recent bound on
concurrence by Mintert--Buchleitner [F. Mintert and A. Buchleitner, Phys. Rev.
Lett. 98, 140505 (2007)]. Relating it to the reduction criterion for
separability we provide yet another proof of the bound and point out some
possibilities following from the proof which could lead to improvement of the
bound. Then, relating concurrence to the generalized robustness of
entanglement, we provide a method allowing for construction of lower bounds on
concurrence from any positive map (not only the reduction one). All these
quantities can be measured as mean values of some two--copy observables. In
this sense the method generalizes the Mintert--Buchleitner bound and recovers
it when the reduction map is used. As a particular case we investigate the
bound obtained from the transposition map. Interestingly, comparison with MB
bound performed on the class of 4\otimes 4 rotationally invariant states shows
that the new bound is positive in regions in which the MB bound gives zero.
Finally, we provide measurable upper bounds on the whole class of concurrences.
