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/ψK +, B 0→J/ψK ∗0 and B 0→D ∗− μ + ν μ decay modes with 0.37 fb−1 of data collected in pp collisions at s√=7~TeV during the 2011 physics run. The opposite-side tagging power is determined in the B +→J/ψK + channel to be (2.10±0.08±0.24) %, where the first uncertainty is statistical and the second is systematic.