A limiter will add loss to the path when input signal is high enough. So yes, both signals will be attenuated. If no suitable filter is at hand, you can McGyver one;
make a 1/4 stub that kills the 8 GHz signal, A SMA T and a short piece of semirigid to be cut and grinded to suitable length, You need a network analyzer to get it right, or at least a spectrum analyzer + white noise source.

Some loss will occur at 4 GHz also, so the stub filter needs to be characterized. Also, your test object might respond poorly to total reflection of the 8 GHz signal, pad with 10 dB in front of the filter. Is it for measurements or for usage ? Lowpass filters are reasonable priced at mini-circuits.

Thank you for your response. This is indeed for measurements. The problem is that those frequencies change from device to device -- I was hoping to find a broad-band solution. Well, it seems I will have to buy a couple of filters to cover the variety of DUTs. The semirigid stub is a nice idea though. Thanks!

I think lowpass filters are the most economical way to handle this. You have to analyze the variety of DUTs and see that you get a filter for each flavour, taking in account not only that the lower freq is within the passband byt also that the higher freq gets attenuated enough.
There are tunable filters, quite expensive things. A bandpassfilter covering the low freq of all DUTs could be possible.
Another approach could be a diplexer if one is to be found that suit all types of DUTs. This would give the advantage of possibility to proper terminate the unwanted signal into 50 ohm, like this one: https://www.markimicrowave.com/Assets/datasheets/DPX-0508.pdf

I agree, you need a diplexer to split the signals, then operate on them independently

https://www.microwaves101.com/encyclopedias/diplexers

Steve

You need some frequency-selective component to be able to discriminate between the 2 signals at different frequencies.

LPF filter is the most general solution (works over the widest frequency range).

If the frequencies are known in advance, a notch filter or harmonic filter might work better.

The quarter-wave stub idea is a type of notch filter to create destructive interference at the frequency you want to reject. You could use a tuneable quarter-wave stub if you need the filter to be tuneable, though it'll only notch out one frequency at a time.

A diplexer is a 3-port filter, with a common input and 2 outputs: LPF + HPF, typically with less insertion loss than splitting the signal and filtering each signal individually.

You can make a poor-man's diplexer:
Though you're relying on the LPF to reflect the out-of-band signals at the input port, which isn't always the case for LPF filters.

you can add a resistive frequency equalizer that has 0 dB of loss at 4 Ghz, and 20 dB off loss at 8 ghz.
If you think of a quarter wave short circuit stub at 4 GHz, you can add a resistor between it and the main line. Since a short circuit transforms to an open circuit a quarterwave away, that resistor will not absorb power at 4 Ghz. then at 8 Ghz that same stub with the short circuited end will be half wave long, and the resistor will absorb 8 Ghz energy. You can adjust the resistor value to get the 8 Ghz attenuation you want to. You will need to use small resistors, like 0402 size.

there IS such a thing as a frequency selective limiter, where it will attenuate a big signal while barely attenuating the small signal at a different frequency. they are not commercially available that i know of though.