Can general aviation use UHF to contact ATC?
The UHF air band operates in AM in a general range of 225.0–399.95 MHz. Many ATC functions have both VHF and UHF frequencies. For example, Newark Liberty Tower uses 118.3 and 257.6. ATC will often broadcast on both the VHF and UHF frequencies.
You can look up these frequencies on the FCC frequency allocation table to see who is allowed to use these frequencies. This is also located in CFR Title 47, §2.106.
According to the table, the the non-emergency allocation of these frequencies is Federal use:

In the bands 225-328.6 MHz, 335.4-399.9 MHz, and 1350-1390 MHz, the fixed and mobile services are limited to the military services.
The bands 235-322 MHz and 335.4-399.9 MHz are also allocated on a primary basis to the mobile-satellite service, limited to military operations.

There are no non-Federal uses cited for those ranges. Also, per Title 47 §2.102(c):

Non-Federal stations may be authorized to use Federal frequencies in the bands above 25 MHz if the Commission finds, after consultations with the appropriate Federal agency or agencies, that such use is necessary for coordination of Federal and non-Federal activities

So it seems that if you don't have a military purpose, outside of special agreements you are not allowed to use these frequencies. For more information, the National Telecommunications &amp; Information Administration (NTIA) has reports on the usage of the lower portion and upper portion of this band.

Technically there are also limited non-Federal uses but they don't apply to this question:

The frequency 243 MHz is the frequency in this band for use by survival craft stations and equipment used for survival purposes.
...may also be used, in accordance with the procedures in force for terrestrial radiocommunication services, for search and rescue operations concerning manned space vehicles.

For the gap in the ranges mentioned above:

The use of the band 328.6-335.4 MHz by the aeronautical radionavigation service is limited to Instrument Landing Systems (glide path).

And additionally for 322-328.6 MHz:

...all practicable steps shall be taken to protect the radio astronomy service from harmful interference.