The paper describes observations of singularities in freely propagating microwaves of fixed frequency. The wavefield studied has a clear propagation direction and this is used to define transverse electric and magnetic fields. It contains singularities both of the transverse and also of the full electric and magnetic fields. The positions of these confirm predictions that the singular features of the electric and magnetic fields are not in general coincident in space. A non-rigorous, but practical, characterization of lines of transverse circular polarization (C lines) as strong or weak features of the waves is introduced. It is shown that strong electric and magnetic C lines are generally close to one another, whereas weak C lines are often close to lines of true circular polarization of the full electric or magnetic field.