TE, TM and TEM modes ...

I have been under this impression for quite some time that in microwave range all devices (waveguides, bends, coax cables) propagate waves in TE or TM mode. By microwave range i mean frequency range about 4 GHz ... is it really so ? Or we can have wave propogation in TEM mode even in microwave range ?

It's certain that you have TEM modes in some kinds of transmission lines such as parallel plate lines, striplines etc. Of course there are other devices like microstrips and slotlines in which the propagation mode looks like TEM but it's not TEM , so it is called quasi-TEM. So, if your device works in the microwave range I think that you can have TEM modes there too...It has to do with the geometry of your structure..

Let say the wave propagates in z-direction; if you have E and H in only x and y direction, you have TEM wave. This is true for any frequency range. The question is how can you know that you field have which components (x, y or z). The simulators have a good visualization tools so that you can see the fields in vector form and you can know now what kind of wave you have.