Her brother Przemysł I of Greater Poland married Elisabeth, daughter of Henry II the Pious.
Another brother Bolesław the Pious married Helen, daughter of Béla IV of Hungary.
Euphemia's only sister, Salome of Greater Poland married Konrad I, Duke of Silesia-Glogau.
The couple were related in the fourth degree, so they needed a papal dispensation in order for the marriage to be considered valid.
The marriage was to help bring closer ties between the two Piast branches and for political reasons to do with Euphemia's brother Przemysł.