At that frequency, you'll have to use waveguide. Some rectangular waveguides in that range would include WR-5.1, WR-4.3, and WR-3.4 (e.g. see VNA extenders here: http://vadiodes.com/en/products/vector-network-analyzer-extension-modules)
If you want to cover the full octave bandwidth (1 mm - 2 mm) at once, then you'll probably have to used double-ridged waveguide. I don't believe the standards for these are that well established, and I would imagine you would have to make some tapers/transitions to interface with any test equipment in bands, like those above.
Thank you for your valuable reply, i want to know that generally, we use SMA female connector to feed the patch antennas, but when we design millimeter wave antenna like dimensions are 1 mm x 2mm or may be smaller, then what we can do? and the method of their testing?
Well, it all depends on your operating frequency. SMA is no good above 26.5 GHz, generally. When you said 1-2mm, I assumed you meant that was the wavelength (in free space), corresponding to about 150-300 GHz. If, instead, you mean that the antenna is 1-2mm in size, perhaps half a wavelength or smaller if used on a high-dielectric constant substrate, then it could be below 100 GHz.
Up to 110 GHz, you have the option of using 1mm coax -- but I can tell you from experience that the connectors, adapters, and cal kits for measurement are EXTREMELY expensive, and frankly don't perform very well. (I had to test a part once in 1mm coax where the performance of the part was far better than that of the test adapters, making the test practically meaningless). I wouldn't recommend it.
Really, for anything above 50 GHz, I would use waveguide. Waveguide to printed-circuit launchers can be made, but are typically custom. If you're geometry just wouldn't support a waveguide housing, then the best I can suggest is to test your antenna on a wafer probe station. Mm-wave wafer probes are readily available, but depending on what you want to measure (beam pattern, etc.) the geometry could be awkward.
Most SMA won't quite make it to 30 GHz. If it were me, I would use 2.92mm connectors (e.g. http://mpd.southwestmicrowave.com/products/family.php?family=87)
What is the inner and outer dimensions of 2.92 K connectors and what is the isolator material of the K connector for CST software ?
For 3.5 mm connector it is Teflon material with 2.1 dielectric constant but for 2.92 mm i think it must be a subtrate with more higher dielectric constant like 7. What do you think?
Still do not understand clearly. For 28 Ghz - 40 Ghz frequency band, it is better that we design a SMA connector for obtain the closest results like real, or not ?
It is better to model an SMK connector for 26.5 - 40 GHz. The datasheet can be found with the supplier of the connector on their website in which they have defined the dimensions and the materials assigned to each component of the connector like in this case, these are southwest connectors and their datasheets.
Depending on your structure SMA-K connector and End launchers (you dont need to sold, you have to fix it with screw nuts) can be used in mmWave antennas.
There are multiple coaxial connectors suitable for high frequency (mm-wave) applications. However, you must consider the facility and the coaxial adapters which you are gonna use to measure the S11 parameter. For instance, mini SMP connectors are cheap and can work up to 40 GHz. Yet, you cannot directly mate a mini SMP with K-type (2.92mm) connector inserted in VNA, unless you have a very expensive mini SMP to K-type adapter in your facility.
Thus, my advice is to go with K-type (2.92mm) connectors, which are prevalent in the market and most of the distinguished antenna labs.