The calibration and performance of the opposite-side flavour tagging algorithms used for the measurements of time-dependent asymmetries at the LHCb experiment are described. The algorithms have been developed using simulated events and optimized and calibrated with B+ -> J/psi K+, B-0 -> J/psi K*(0) and B-0 -> D*(-) mu(+)nu(mu) decay modes with 0.37 fb(-1) of data collected in pp collisions at root s = 7 TeV during the 2011 physics run. The opposite-side tagging power is determined in the B+ -> J/psi K+ channel to be (2.10 +/- 0.08 +/- 0.24) %, where the first uncertainty is statistical and the second is systematic.