If you want to permanently remove the saddle valve, you could cut out the saddle valve and rejoin the pipe with a repair coupling. A repair coupling is basically just a short length of pipe (usually in lengths of 6" or 12"), but the size of the pipe is the size of a fitting rather than the size of the original pipe. A repair coupling would be the quickest way to bridge the gap if there is enough play in the pipes to slip the coupling into place. If not, the other alternative would be to use slip couplings (couplings with no stop in the middle). Make the gap where the saddle was located at least the size of a slip coupling and cut a length of new pipe almost exactly the size of the gap. Then use the gap to give space to get the slip couplings on the pipe, move the slip couplings out of the gag, insert the new piece of pipe in the gap, and slid the couplings in place to solder the whole thing together.

If you don't want to hassle with removing the saddle AND the tubing coming off the saddle is copper and you just want to permanently but reliably cap it off, cut the copper coming off the saddle at least 6 inches away from the pipe and then solder on a cap rather than use a compression fitting. That way, if someone wants to reuse the saddle valve to feed a new refrigerator, they can cut the cap and solder new tubing to the 6" stub coming off the saddle valve.

Well, if your compression cap is not leaking, it's okay - for today. But, it seems like all saddle valves eventually leak whether open or closed so I would get rid of the saddle valve assembly in it's entirety as soon as you can swing it.

I know of no good way to patch a hole punched into the copper pipe. IMO, the best way is to either a) cut out 6 inches or so of the punctured copper and repair with two repair couplings (no bump in the middle) and a short piece of copper or, if possible, b) cut out only the inch or less of affected pipe, sweat in a "T" and cap off the unused stub.

Good luck.

Ha! Hookoodooku can type faster! :)

Great ideas, thanks a lot for the advice. I think I will get rid of the saddle valve altogether - but it will have to wait about a month or so maybe. So, hopefully that compression cap will last and the valve itself doesn't start leaking! Thanks, again!

If what you have now with your compression cap is working I would leave it alone, if you think that you have probs. then you will have to cut out the tube where the saddle valve punctured the line; a small piece of copper, two slip couplings, and four solder joints, I don't know what your expertize is, to me its cake, lots of luck.

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"If all else fails, read the directions"

Cut out the valve and instal a single slip coupling. You may have to look around to find an actual slip coupling. They do not hava a stop in them and will slide all the way down the pipe.
No reason for two unless you cannot move the pipes enough to get a single one in (and even then two will not be much easier).