There is an interesting YouTube video about how car thieves steal vehicles. Apparently, these new systems where the car recognizes your key-fob and then allows you to open the doors and to start the vehicle by only pushing a button and not having to use a key, can be defeated by using a two box radio system that two thieves working together in cooperation can use to steal your vehicle.
What it consist of is one box that one thief holds outside your house near your house wall (usually they start by trying near your front door because usually people place there key-fob in the house near the door), and that first box picks up the signal from your key-fob, and relays the code information by a different radio frequency than your fob is using, to a second box that the second thief holds near your vehicle. And with that code stolen through the wall of your house from your key-fob they are able to emulate the signal from your key-fob and the vehicle things the valid signal is being sent and allows them to enter, and start, and drive your vehicle.
So there are a couple of things you can do to prevent the radio signal from your key-fob from being accessible to would be thieves.
1) Do not keep your key-fob near the front door, and even better would be to not keep it near any outside wall at the level that would be easy to access from outside the house. In other words keep them on an upper floor, and towards the center of the house, away from the outside. The further away you keep them from where someone outside the house could access the signal from them, the better.
And or 2) Keep them in a Mu-metal box. Mu-metal is any metal that blocks radio signals. Different metals have different amount of ability to absorb radio signals. Radio signals propagate by means of a combination of magnetic and electrostatic waves. Metal that can conduct both magnetic waves and electricity makes good Mu-metal.
Special Mu-metal is made of combinations of Nickel and Iron, and or Iron, and silver, and or Iron and copper, and other combinations of Iron, silver, and copper. But you do not need special Mu-metal to stop the signal from your key-fob. Plain steel or even tin can work to some extent. And if it is thick enough it will do the job.
One thing that comes to mind as probably a good Mu-metal box is a good old fashion cast iron Dutch-Oven with a cast iron lid. The thick iron walls it has should work well to block radio signals from a key-fob. We had one of those laying around the house for several years and since no one was using it, I gave it to one of my brothers. Oh well, there are other metal boxes that will work for this job.
I tried a used cookie tin that Christmas cookies came in because it is probably made of cheap thin steel and we have one left over from Christmas. And we have an old small silver jewelry box with thick walls about 1/8 of an inch thick that no one is using and it is big enough to fit my key-fob in so that also should work. I put my key-fob in the small silver jewelry box, and put that jewelry box in the cookie tin, and held it close to the outside of the door of my vehicle near the arm rest where the antenna is built into the control in the door lock button, to see if it would still pick up the signal from the key-fob. And the vehicle would not let me open the door. So even with the fob right next to the door, the signal is blocked well enough to not be detectable when it is in both of these boxes at the same time. Interestingly, when I tried each of them separately with the fob in them they did not block the signal well enough and I was able to open the door. So I use the two boxes together as my Mu-metal box for my key-fob.
So, if you put your fob in a thick enough box or boxes so there is enough metal around it, you can block the signal so thieves can not steel your vehicle.
BTW, I have a second Key-fob that I keep upstairs with the battery removed from it so it also can not be accessed to get the code for the vehicle.