Pipetting apparatus has a block for holding pipette tips and connecting to pipette cones of a multiple-pipette head of a liquid handling apparatus. The block has cavities in an array and pipette tips inserted therein as well as conical plug-in openings for pipette cones of a multiple-pipette head. The block additionally has devices for connecting the block and the head. The block has receptacles with a shoulder and inserts for inserting into the receptacles, insert having a cavity, a cylindrical insertion opening with inserted pipette tip and a conical plug-in opening for sealing introduction of a pipette cone. Each insert has a support with which it rests on the shoulder of a corresponding receptacle when inserted into the block. Preferably each insert lies in the corresponding receptacle of the block with horizontal play on all sides.