Magnetic contributions to the interaction of ordinary matter with pionium,
i.e. exotic atoms formed from oppositely charged pions, are calculated expl
icitly in the context of the experiment DIRAC at CERN. These contributions
have previously been estimated to amount to about 1% of the complete cross
sections. Since this experiment requires the cross sections for electromagn
etic processes at the 1% level as an input, a justification by explicit cal
culation of the previous estimations is necessary. We also estimate the mag
nitude of relativistic effects particularly for the electromagnetic couplin
g of the pionium system to the target system. These effects turn out to be
negligible.