The design and properties of a new cryogenic set-up for laser-microwave-laser hyperfine structure spectroscopy of antiprotonic helium - an experiment performed at the CERN-Antiproton Decelerator (AD), Geneva, Switzerland - are described. Similar experiments for (4)He have been performed at the AD for several years. Due to the usage of a liquid helium operated cryostat and therefore necessary refilling of coolants, a loss of up to 10% beamtime occurred. The decision was made to change the cooling system to a closed-circuit cryocooler. New hermetically sealed target cells with minimised (3)He gas volume and different dimensions of the microwave resonator for measuring the (3)He transitions were needed. A new set-up has been designed and tested at Stefan Meyer Institute in Vienna before being used for the 2009 and 2010 beamtimes at the AD.