I was recently thinking, that this amulet has too much power for an item with uncommon rarity, and there should be a way to bypass its feature, except the dispel magic. It basically blocks the whole school of divination magic. However, after searching for a couple of hours I haven't found any way to do it. So maybe you, guys, know about any options of how to bypass the Amulet of Proof against Detection and Location? Maybe there're any blind spots hidden? 

Ways to bypass an Amulet of Proof against Detection and Location exist by suppressing its magic via spell like Antimagic Field or dead magic zone in Forgotten Realms.

Or by using abilities that are not magical in nature but that let you locate creatures, such as a Ranger's Feral Senses.

Yes, if you use Antimagic Field or dead magic zone in Forgotten Realms, the amulet won't work, but neither any spells will work in this area, including divination magic.
And Ranger's Feral Senses is more about invisible creatures, but not hidden from divination.

If the wearer is a celestial, fiend, or undead, a Paladin's Divine Sense could also locate it.

A Wish spell could also potentially work if DM allow it.

I don't know if I would call this item's effect OP considering it achieves the same effect as the 3rd level spell Nondetection which doesn't need Concentration and lasts 8 hours.  Divination is insanely strong for the level at which you get it IMO.  If it is so easy to do, it makes sense that blocking it would be just as easy.

Depending on how precise a location you want, could you search for his saddle, saddle bags, horse, or something else that would get you in the ballpark? What about his weapon, staff or musical instrument? Anything personal that might not always be on his person should do.

Bypass it by, well, bypassing it. :-)

Instead of scrying Conan, who is protected by such an amulet, scry Conan's companion Malak. Or Conan's horse. Sure, you can't see Conan through your crystal ball, but if you see Conan and Malak's horses walking while Malak talking to someone you can't see, then you can be reasonably sure that Conan is there.

Also, remember that someone wearing the amulet will not be casting augury or comprehend languages or detect magic, or any other "Target Self" divination spell. Also, no-one will be casting guidance on them. It's a good item but it has its downsides.

Yeah well, but what if you haven't seen a person you're looking for for a long time, and don't know what stuff he/she has, to scry through the items? 

Also, will he/she be hidden from your site, while you're scrying through the object?

I know, I'm overcomplicating the task too much, however, was hoping to get a 100% solid solution. 

Whoa! That's a fair point, haven't thought about that. 

If you are looking at it from a general power level POW then you also have to consider that it uses up one of your attunement slots for a fairly niche gain.

Sending. Sending is an evocation spell and isn't blocked by the amulet. Depending on how your DM rules your perception on if a spell works/connects to its target or not, it could be used to tell if someone is still alive or not. It doesn't particularly tell you where they are but it could help. 

Thanks! Not quite what I've asked about, but still very useful for me! 

This would be up to the DM, but notably, the amulet specifically says "You" meaning the person attuned to the amulet are protected. There is a world where you can argue RAW and can do divination to find objects the creature carries or are with, specifically the amulet itself. Especially if you have a Locate Object spell. That is not to say that your equipment is visible on an invisible person if a Scrying target sees you, but the amulet only says that you are unable to be targeted or seen through magical sensors.  

If nothing else, if you know nothing about the person, if it has been a LONG time and you don't know anything about who they are with and what they have you will know that they have the amulet.

Scrying also lets you target a location, so if you know where they usually hang out you can scry on that place and if you see things being moved by something invisible you can assume your target is there. 

Quote from ConalTheGreat >>

This would be up to the DM, but notably, the amulet specifically says "You" meaning the person attuned to the amulet are protected. There is a world where you can argue RAW and can do divination to find objects the creature carries or are with, specifically the amulet itself. Especially if you have a Locate Object spell. That is not to say that your equipment is visible on an invisible person if a Scrying target sees you, but the amulet only says that you are unable to be targeted or seen through magical sensors.  

If nothing else, if you know nothing about the person, if it has been a LONG time and you don't know anything about who they are with and what they have you will know that they have the amulet.

Scrying also lets you target a location, so if you know where they usually hang out you can scry on that place and if you see things being moved by something invisible you can assume your target is there. 

 But you wouldn't be able to scry for "the amulet that X is wearing", because the spell can't see X.

Soul cage is a necromancy spell that has an effect that allows you to create a magical sensor that gives you information about a place that you can name that the killed creature has seen in its life. If you know someone who knows your target you could say something like "Your home base" and see if your target is there.