Veiled visitations are used in those times when Jesus chooses to come and talk to someone but not reveal who He was at that moment. We might never understand why or even know that we have had one, but that does not mean that it was not an encounter. The Bible tells us that this can also happen with the angels and that we might be entertaining angels without even knowing it. This would also be a veiled visitation.
I do not have any personal modern examples of this, but have heard others speak about having them. You will find many books about the angelic where people have encountered angels in ordinary situations but have not realised it until afterwards. The response for most after this type of visitation is "I think that I just spent time with an angel," or "I think that was Jesus I just spoke with." Some never know while others feel they know for sure. I have the ability to see in the Spirit so I have always wondered if I would identify them during the encounter, but this is just a personal question. If it ever happens I will make sure that I share it.
I put Veiled Visitations with Christophanies and Theophanies because it seems that neither form of encounter are currently very common. While Christophanies and Theophanies are more typically experienced with the prophetic office that does not mean that only prophets will have those encounters. Jesus has the right to visit whomever He chooses. Veiled Visitations are for anyone whom God needs to speak to in a different manner, regardless of whether you walk in the prophetic office or not.
I really believe that the closer we get to the end of the age the more we will see these types of visitations, even if we do not know for sure if it was Jesus or an angel we spoke with.
Timothy, author and friend of God, shares out of a place of daily walking face-to-face with the Lord, encountering both the angelic and the saints of old, seeing and understanding things from a heavenly perspective.