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The upper limit depends on how long your signal traces are going to be, and the exact type of FR4. The limiting factor is the dielectric loss (sometimes expressed as loss tangent).
In traditional FR4, above about 1-2GHz, dielectric loss becomes more significant than copper losses such as skin effect. You begin to lose several percent per inch in signal strength, and the propagation delay increases because of the frequency dependence of the dielectric constant of FR4.
Having said the above, it is important to recognize that there are MANY types of FR4. The designation FR4 simply refers to the flame retardant capabilities of the resin/glass composition of the board material. There are many variations of resin and glass mat, and some have excellent dielectric properties. I have used FR4 materials with a dielectric constant of 3.7 at 1GHz. Such material can easily handle moderately long signal paths in the range 5-6GHZ without significant signal degradation.
Bottom line - the upper frequency limit depends on exactly what brand and type of FR4 you are using, how long your signal path is, the rise time of your signal, and how much loss your application can tolerate. Once you determine your signal needs, talk to your board fab and see what is the best FR4 material they can offer. Generally, high Tg FR4 will have better dielectric properties than so-called "normal FR4". If your fab doesn't have a recommendation for the best FR4, ask to see the data sheets for whatever high Tg material they offer.
Well known Slovenian radio-amateur, dr. Matjaz Vidmar, S53MV, use FR4 for
his SHF radios up to 10ghz.
A practical FR4 laminate thickness for microwave circuits with SMD components is probably 0.8mm. A 50-ohm microstrip line has a width of about 1.5mm and about 0.2dB/cm of loss at 5.76GHz. Therefore microstrip lines have to be kept short if etched on FR4 laminate. For comparison, the FR4 microstrip losses are about three times larger than the microstrip losses of a glassfiber-teflon board and about ten times larger than the losses of teflon semirigid coax cables.
Although FR4 laminate losses are high, resonators and filters can still be implemented as microstrip circuits. Considering PCB etching tolerances and especially underetching, both transmission lines and gaps in between them should not be made to narrow. A practical lower limit is 0.4mm width for the transmission lines and 0.3mm for the gaps.
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