In many books the permittivity of a material is only listed as dielectric constant for one or a couple of frequencies. 1 kHz is used often (for example in the Plastics Technology Handbook, 4th ed, ISBN-13: 978-0-8493-7039-7), but I'm looking for the permittivity for a frequency at least 2000 times higher (2-4 GHz).
How does one calculate the permittivity of a material for a higher frequency? Is the dielectric constant still useful here?
There are a lot of methods for determining permittivities at high frequency, but they are uniformly experimentally-based. One of the easy methods is a resonant cavity. You create a resonant cavity that has a known resonant frequency. Then insert the material inside the cavity by some holder and see how much the resonant frequency is perturbed (using a vector network analyzer or similar equipment). From this you can figure out the permittivity. This is a pretty accurate method but an open probe test can do a reasonable job with a lot less manufacturing.
From experience, there typically is good data on common dielectric materials around the heating frequency (2.45 GHz). It will not likely differ meaningfully for 1-4 GHz.
I've tested microwave cavities with dielectric materials at the 18-20 GHz range and usually published values are fairly accurate for 10 GHz even applied at 20 GHz. It is certainly still a meaningful thing to have!
If you're looking for specific data, I'd look to data sheets from manufacturers of a given material. Matweb is also a good resource - you can sign up for a free account to get full results, I believe: http://www.matweb.com/
Also - just as an aside, doing antenna + dielectric simulations may be pretty easy to test the viability of dielectric materials, depending on the complexity of your antenna geometry. I've used COMSOL and a bunch of other packages to determine applicable relative permittivity / loss tangent ranges for microwave antennas / end launches. It sure beats purchasing expensive materials & manufacturing only to find out your frequency response is poor.
Calculating permittivity as a function of frequency is extremely difficult at best, to the point of being considered so impractical as to be impossible. Permittivity as a function of frequency behaves in response to a many properties of the dielectricum, and does not follow a predictable curve. As you sweep across the frequency spectrum, permittivity of a given dielectricum may go up and down at seemingly random intervals.
If you need accurate data of the permittivity of a given dielectricum under given circumstances (temperature, voltage, mechanical properties etc.) measurement is the only recommended option.
