Considering the idea of a separate meter that measures RF from the antenna:
The practicalities of this depend on A)if you are hoping for a meter that can show signals down to the noise floor of your scanner or if you want something that will detect a 4watt handheld 100 feet away eg for use with closecall. and B) if a 'precise' signal meter is actually any use.
Unless you are in a little valley in the countryside a scanner antenna will always be picking up lots of radio signals, often fairly strong, such as 88-108MHz broadcast stations, pager transmissions, mobile phone signals consisting of fraction of a second bursts, UHF TV transmissions, tetra base stations and aircraft overhead.
When your scanner stops on a signal an s-meter connected to the antenna cable will still be getting lots of other signals as well.
A sensitive wideband signal strength meter will be constantly showing an ambient RF level of something like -60dBm with an indoor antenna or -45dBm with a rooftop antenna and jumping around as flight 207 from Magaluf calls ATC. The ambient RF might be hotter than that if there is a tetra base on a hill beaming towards you or a mobile phone base on a block of flats you can see out of the window.
That could be an interesting project to build anyway but it's not what you are asking for.
You could decide that you will dodge that problem by just making a wideband meter with power ranges above all the ambient stuff. Depending on where you live you might find you could only clearly discern a transmission from everything else if it is at the level of a 4watt handheld a couple of hundred feet away from you (depending on the buildings in the way rather than the distance). There may be 500 kilowatts of UHF TV from a 700foot tower on the horizon.
Ah, but maybe you can use a filter to pull out voice comms traffic eg 136-174 or 440-460 say. That is going to need a carefully arranged filter because VHF has pager transmitters that tend to be very strong going SQUEEEEE-AWWWK and turning on and off every few seconds on 153MHz. UHF has tetra base stations and trunked radio control channels.
You could pull a bandpass filter block out of a 1980's PMR mobile rig (or better rip out the rest of the innards and use the case) to select a few MHz of spectrum. Maybe you are really only interested in, say PMR446, so you don't mind the limited frequency range.
If you need better selectivity than you go full circle to needing a superhet radio receiver with a s-meter, something like a high-end comms receiver or scanner...
A good receiver signal strength meter should show a wide range of received power. On a decent comms receiver the difference between S1 and full scale on the meter will be 60dB or more. That means full scale is a million times more power from the antenna than S1 or a thousand times the voltage. Showing rectified volts on a linear scale isn't much use.
At the low end of the scale you want to make out the difference between 1picowatt and 3picowatts at the other end you want to make out the difference between 1000000picowatts and 3000000picowatts.
So after the bandpass filter you have scavenged from an Ericsson C60 you need a detector and a logarithm amplifier.
One way is some RF amplification, a diode detector and a log circuit using an opamp. That's a pain.
There is a lovely chip that featured in a load of wide range power meter projects a few years back.
The AD8307 from Analog Devices.
It gives a DC voltage out that goes up logaritmically as the input power goes up.
DF7TV has a nice AD8307 based meter design.. That goes down to -80dBM. I think BBC radio 1 would swing that meter over 10% with a bit of wire in the socket at my place.
I bet it needs to be in that metal box to stop it showing a reading when the neighbours baby monitor is on.
With a bandpass filter in front and a couple of "little black dot" MMIC RF amps like a MAR-6 (cheap and easy to use) that would make an interesting receive signal meter.
Another aspect is that you are asking for "precision". To me that means being able make out a couple of dB change. Is that actually any use?
At UHF, using a 'rubber duck' on an handheld scanner inside a house, you can close the door and find the level of a signal changes 6dB, wave the scanner around and a UHF signal can vary 20dB due to multipath.
I have one spot on a shelf where I can get the audio from Channel 5 TV with a rubber duck, anywhere else it fades out.
Local effects are much less of a problem with a rooftop antenna but things still happen at the transmitter end.
If you are listening to a transmitter in a car a few miles away the signal strength changes hugely when the car drives past a huge B&Q warehouse with metal walls that is between them and you or when the car is on one side of a hill or the other.
The signal from a UHF handheld a mile away can change 20dB depending on which way the antenna is pointing relative to you and if the user has his body between the handheld and you.
How about wiring a better signal meter into a scanner?
In some scanners there will be an AGC voltage that can be tapped off easily and fed to a nice big analog meter.
Typically there is dual gate FET in the front end, one of the gate's has a DC voltage applied that control how much it amplifies the RF. It's used to avoid clipping strong AM signals.
Depending on the scanner tapping the AGC might need a buffer amp or it might be fine to connect it through a resistor about about 33K to a 100uA meter movement.
Disclaimer: All numbers are rough guesses.