Seems to me that any physical manifestation of an angel is an adaptation of that being to our senses; nothing about an angel is inherently physical. Only its reflection of God’s power provides the ability of a spiritual creature to take on physical properties.
Therefore, an angel possessing any supernatural glory perceived by the physical eyes (or ears, etc. etc.) would likely be going about some special business.
One could also postulate that a very devout person could become physically or mentally aware of the perceptions of their own metaphysical soul, and thus become physically aware of non-physical beings. Padre Pio comes to mind.
Personally, though, I have suspected the specific presence of an angel (as opposed to the spiritual awareness of God or spiritual nearness of a saint) on a handful of occasions, namely those involving homeless persons. Not to say that a homeless person was an angel “in cognito” (although I don’t discount the possibility) but more likely to say that our charity to the homeless seems to be very connected to the actions of God through His angels.
A certain memorable experience of mine was on vacation in Europe; being somewhat short on cash (since ATMs had heavy charges and I didn’t exchange too much upon arrival), I kept close watch on my wallet’s funds. After counting a specific amount of 20-Euro bills in my wallet (2, if I remember now), I encountered a homeless man on the side of the street. Counting again (and, honestly, with some slight hesitation, as a 20-Euro bill wasn’t something I was sure I was ready to instantly part with), I handed him one of my 20-Euro bills, as I decided that it had far greater potential in his hands than in the hands of an 18 year-old tourist :rolleyes: .
A few minutes later a close friend and I stopped to grab some ice cream. I checked my wallet again, but was somewhat confused; after counting my bills a few more times, I realized that I had the same amount of 20-Euro bills as before I gave one to the homeless man. I was, at first, astounded. Not much of a hugely miraculous experience, but I think God was telling me that in giving away to help others in greater need, I would lose nothing and that He would ultimately provide me with what I needed, sometimes more immediately and physically than other times, perhaps.
Also, a sort of “Doubting Thomas” friend nearby might have gotten a “hole in Christ’s hand” moment, so to speak, from this event. At least, now I know he’s involved heavily in Pro-Life activity and is becoming more active in his high school’s Christian Life community.
Herein, though, lies a problem with trying to publicize private miracles - anyone could claim that I simply miscounted my money at some point. There’s no way for me to PROVE what happened was miraculous, just as someone who encounters a physically-manifested angel cannot probably PROVE what happened to them. We can get into trouble when we start trying to fall back onto this sort of thing instead of faith, Scripture, and Tradition.