I fly a Glasair I FT and since 1987 my engine instruments, either analog "needle" or digital in the later years bounce around whenever I transmit. Worse on some frequencies than others. On some it is completely absent. Can't remember what frequencies but is probably minimal at the center of the VHF band (see comment below about VSWR). The composite airplane offers no shielding from the RF and I haven't found any way to avoid it. Moving the antennas as far as possible aft away from the instrument panel lessens the effect. The antennas are all copper foil (al la RST Avionics plans) with 3 ferrite beads just before where the coax is soldered to the foil dipole arms. The VSWR is low at the mid-band frequency and goes up at each end of the VHF band as would be expected but stays around 2:1 so some RF is travelling down the coax reflected from the connection point to the dipole but no worse than any other installation as far as impedance matching.
I have tried filters on the power leads into the instruments but that has no effect so I don't believe the RF is getting in on the power wires.
I even did a ground experiment in which I disconnected the airplane antenna and connected the radio via a long coax to an identical external copper foil antenna about 20 feet away. The problem nearly went away so it is a radiated energy problem, not bad grounding/shielding of the power wires, etc.
For the analog instruments the RF is probably getting picked up by the meter movement coil directly and for the digital ones it is probably swamping the front end amplifiers or something like that.
If I point the end of my handheld radio antenna at an instrument, the reading bounces around also.
I consider this to be a "cosmetic" defect only, as it is not absolutely necessary to be able to read the CHT, EGT, amp meter, etc. for the brief instant that one is transmitting. I stopped trying to "fix" it long ago. Maybe for a certificated airplane that would not "fly". I did the RF interference test on my Garmin 430W IFR GPS at the 4 frequencies that you are required to perform it at and it would lose lock somewhere near the end of the 30 second time period that you have to perform the test. It re-locks with seconds of lifting up the transmit switch. What am I going to do, never fly IFR with the Garmin 430W? I never transmit for 30 continuous seconds during an IFR approach so in real life it will never happen. FAA over-regulation for certificated aircraft in my opinion and that is why I fly a homebuilt.
My DYNON is a little D6 and it never does anything unusual for some strange reason when I transmit. Strange but nice!