I think SILENCE is appropriate here.

Well if they are a really good friend they should know your beliefs. I'd just smile and say "Can your guardian angel watch over me"?

In Biblical reference angels are gods nuclear weapons / soldiers. If an angel shows up it usually heralds death destruction or crazy events. So when people talk about angels watching over them they are not reading their crazy book correctly. Plus it is all nonsense anyway.

I think the best approach is either ignore or just ask questions. Have you ever watched the Athiest experience on Youtube? The hosts often ask Theist callers. "How they know?" "What evidence do they have" it usually boils down to "I just Know" or "I have Faith" and that is where the discussion ends. edit: Another question may be: How do you know this isn't an agent of Satan who is trying to deceive?

Let people have their delusions as long as they don't take stupid risks because of it. I've known two very nice ladies who thought god talked to them, They didn't try to drag me to church: I didn't cry BS. If that's what they need to believe to face tomorrow so be it, neither of them were judgemental and they tried to help other people, but they'd both had a hard life when they were younger, one horrendously so.

I used to believe the same. I even invoked my guardian to protect me. Much of my life has seemed as if I had a guardian. Is there a real guadian angel? Not in scripture but mentioned by many ministers to get reactions from you. In truth the guardian is likely a "higher" you than anything else. This puts a higher power into a mental direction.

Does she know you're an Atheist?
If she does - she's kind of yanking your chain.

Also some people who believe in angels do so from a entirely superstitious slant. Kind of like knocking on wood.
I still say "Knock on wood" even though I have absolutely no belief in it? It's just habit.

You could ask her "So do you still look both ways when you cross the street?" (Despite having this guardian angel?). That seems pretty harmless to me and it would open a dialogue.

Having known many different types of people, I've come across some who seem to need their pain. Even if the doctor says they're fine, they still complain that they hurt. This applies to both physical and mental pain. Why can't it be the same for those who feel comfort in much the same way? I agree with kimba that if your friend isn't taking stupid risks I don't see a harm in letting her have her belief, and hope she would let you have yours. So my advice is to allow her her beliefs.

I posted a song yesterday before she sang she said. (Paraphrased) it's okay if someone has an invisible friend who tells them what to do but if your your invisible friend is telling you to tell me what to do we're going to have a plroblem. So my take on you dilemma is to first opt for a live and let live approach till it's not.?

Tell her that you are her guardian Angel

When I was living in Omaha, Nebraska, briefly, there was this mexican gang that called me 'the guardian anglo'...haha...does that count? Those guys were awesome. But seriously, we do a lot of things to feel safe in this world, this one seems to be pretty innocuous, whether it is true or not. If she knows how you feel about it, I would think you could tease each other about it. Or at least, that is how my friends work.

If she believes it, then what she believes is true for her, since we contribute to creating our own universes.
Besides, Einstein showed that all matter is a form of energy, so since energy can neither be created nor destroyed, we have always existed and will always exist in some energy form. No reason to think energy beings don't exist, and quantum physics already proves that multiple dimensions exist.

“I regard consciousness as fundamental and matter as derivative from consciousness." – Max Planck, theoretical physicist who originated quantum theory, 1918 Nobel Prize in Physics

My best friends are Christians and will occasionally ask for prayers in our group texts. They know my feelings about religion. I’ve told them I don’t believe in praying to a god but that I’ll “send out positive intentions in the universe” for them. It just depends on how close you are to this person and if they accept you for who you are. I would generally not engage in the conversation with her unless she is insisting on it.

I have a newer friend that goes "rockhounding" with me, he believes crystals have energies and basically "magic" properties. He used to bring it up more to me which wasn't a ton, but I pretty much remained silent or asked questions expressing doubt but I never just said it's bullshit. He hasn't brought it up in a while now. Maybe just say you arent religious and leave it at that, and try to change the subject in the future. They will catch on if not a complete dunce.

Unless she's doing stupid, dangerous stuff because she has supernatural protection, let it slide.

Is there any need to approach it? Unless maybe she seems to be trolling for validation -- in which case I'd simply say that I don't share that belief but she is welcome to it if it comforts her. I would deliver words to this effect without a hint of condescension and move on to topics you do have in common. If she doesn't get the hint or becomes offended then it wasn't a sustainable friendship to begin with.

My wife, who is way kinder than I am, would probably be curious and ask questions and play along. I think it is the journalist in her. One time we visited a location where a lot of UFO activity supposedly takes place and were approached by people eager to share their alien abduction experience. She practically did a full interview with them, left them feeling really special and obtained an invitation for us to join them with night vision glasses that evening looking for UFOs in the sky.

This was early in our relationship and frankly I was a little alarmed, until we got off by ourselves and she dissolved in gales of uncontrollabel laughter.

We never did take them up on the invitiation due to incliement weather, but her willingness to go all the way in playing along is very different from me (and I'd wager most people).

Some years ago, it was a popular New-Age fantisy to claim to have a "Spirit Indian Guide". I was difficult to that with a straight face inasmuch as I doubt the the "spirits" of deceased Indians would give a flying f.... over the well-being of a member of a racial group that had perpetrated genocide upon them. If there is anything as a guardian angle, they seem to be doing a poor job inasmuch as most people have one or more very bad episodes in their lives.

I would be telling her that my guardian angel is an atheist.

Some people just can't give up their imaginary friends. Not much you can do about it.
If you value the friendship, as it seems you do, roll your eyes and keep on truckin'.

Don't aproach it unless she litterally puts you on the spot and asks you if you believe in that crap.