  We describe a method for computing the Cassels-Tate pairing on the 2-Selmer
group of the Jacobian of a genus 2 curve. This can be used to improve the upper
bound coming from 2-descent for the rank of the group of rational points on the
Jacobian. Our method remains practical regardless of the Galois action on the
Weierstrass points of the genus 2 curve. It does however depend on being able
to find a rational point on a certain twisted Kummer surface. The latter does
not appear to be a severe restriction in practice. In particular, we have used
our method to unconditionally determine the ranks of all genus 2 Jacobians in
the L-functions and modular forms database (LMFDB).
