don't do what I did
Man, I sympathize with you. I had the same problem. I cut the line and let it drain for 2 hours, but STILL had drips coming down every now and then. Some bits of advice (I am risking getting laughed at, but what the heck):
1) Don't apply a torch even when the water is only dripping intermittently. My water was evil, and actually waited until I heated up the pipe good n' hot and then would start trickling again. Of course, the water drew all the heat from the pipe, sending drips of boiling water right onto my head.
2) Don't use rye or wholegrain bread to temporarily clog the line. The seeds clog the aerators and are a pain to pick out. Use white bread only (or an english muffin). I used these and they worked like a charm.
3) Don't use the Oatey gels. It's extremely difficult to get the copper ends smooth enough such that they won't cut the gels when you insert them. When they get punctured, not only do you have to throw them away, your hand gets annoyingly oily.
4) If you're inserting a tee into an existing line, I suggest cutting out a longer section than necessary, and making a longer replacement section out of a slip coupling, a new section of pipe, and the tee. Solder that contraption on the ground and slip it over the cut out. Solder one side to the existing line, then when it cools, wrap it with a moist rag, and do the other side. It's easier than doing both sides of the tee at once (for a novice like me). Also, having a bigger cut out gives you more wiggle room to get the new fitting in.
5) While you are at it, off of the branch, since you now have all the water drained out, run an extension of the pipe down to the ground, with a shutoff valve. Now, if you ever have to drain the water again, it'll be a tad easier to drain the line through this new low point.