Cupid Arrow

Cupid Arrow (キューピッドアロー) are stores known to sell wedding rings, but had recently started expanding by November 10 of the timeline. The head store is found in Oahu, Hawaii.

Principles
The store sells wedding rings, which has them have an external detective agency perform a background check on the customer before they would make an engagement ring or wedding ring for them. For lovers that are in a less serious relationship, tag rings are offered as a substitute.

The rings are made of titanium. The titanium can be colored using electrolysis when it's in a solution. If two rigns are manufactured with the same equipment, the pattern of the coloration comes out so the two rings connect. It is seen as a charm to prevent partners from cheating.

Hawaii Invasion Arc
Mikoto buy the rings from the store after marking its location on her cellphone after the New Honolulu International Airport terrorist incident. She outright states that when she heard that they were going to Hawaii, she though that she could stop by and buy Cupid Arrow tag rings when she had the time.

Despite not yet being Touma's girlfriend, let alone have yet to even confess to him, Mikoto attempts to give Touma a tag ring several times during the arc. When she had the chance after the events of the invasion of Hawaii by Trident, Mikoto is unable to give a tag ring to Touma after she discovers him infuriated with Leivinia Birdway's betrayal and desire to amend it. The narration implies that Touma may have not leave the rest of the group, specifically Mikoto alone, if she had given him the ring.

It can be assumed that Mikoto still has the rings in her possession.