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+, B0→J/ψK∗0 and B0→D∗-μ+νμ decay modes with 0.37 fb-1 of data collected in pp collisions at [Formula: see text] 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.