We have performed Laser-microwave double and triple resonance experiments on clouds ofBa+ions confined in a Penning ion trap to induce and detect electronic and nuclear spin flip transitions. We used collisions with buffer gas molecules in the trap to cool the ions to the ambient temperature and to quench a long lived metastable state, in which population trapping might occur. Loss of ions from the trap by collisions was prevented by coupling the magnetron and reduced cyclotron motions by an additional r.f. field at the sum frequency of the two motions. Electronic Zeeman transitions in138Ba+and135Ba+were observed at a transition frequency of 80 GHz in a 3 Tesla B-field with a fractional uncertainty of3.10−9.From the magnetic field calibration by the cyclotron resonance of electrons stored in the same trap thegJ-factor for both isotopes could be determined to2.10−8.From radio frequency induced&Dgr;mI=1transitions in137Ba+the nuclear g-factor could be determined to5.10−6.Both measurements improve earlier results by about one order of magnitude. ©1999 American Institute of Physics.