I will show you how to replace the antenna without replacing the base.
UPDATE: Be sure to remove the antenna before going through the car wash.
I took the car to Saturn to get a free oil change. They wash every car after service. When the car came out it had no antenna. They replaced it with the correct factory antenna and base.
Step 1: Prepare the Base
Step 2: Prepare the Bolt
Tighten the first nut hand-tight down against the antenna base.
Then tighten the second nut against the first. Turn them tightly against each other to lock them in place.
Remove the bolt from the base and put two more nuts onto the bolt. repeat the tightening process. Be sure to tighten them against each other, but do not tighten them more than hand tight against the first set of nuts.
Once the second set are very secure, loosen and then move the first set out of the way.
Measure the depth of the bolt socket (after removing the remains of the shear bolt) with a piece of wire or another bolt. Mark the first bolt adding the depth to the length of the socket you already marked with the two nuts. And cut.
Step 3: Solder the Bolt Into the Antenna
Wrap the bolt with a large amount of solder and place it in the end of the antenna.
Heating the bottom of the antenna, not the solder will cause the solder to melt into the bolt socket of the antenna. One thing I ended up doing that is not pictured is (while the antenna was still rocket hot) I fed a 2 foot long piece of solder into it. The solder melted and filled the socket to the top. I applied more heat and then pushed the bolt into the antenna.
Leave the antenna to cool for quite a while (I went for dinner) and then remove the nuts from the base.
You now have an antenna that will screw into the base.