This short story was in a Sci-Fi or Fantasy anthology I read in the late 1960s. It involves a scientist who invents a small device with a circular cable loop that is capable of slowing time almost to a standstill for anyone inside the cable loop. The scientist's bad-guy lab assistant steals the device as well as the scientist's daughter and disappears. Using a second time device, a detective, hired by the scientist, pursues the bad guy into the time-stopped, motionless world to which he ran. Ultimately the detective reclaims the device and rescues the girl. They become very close during their time together and ultimately are shifted back to normal time with a humorous result.
Additional note based on comments: a small portable box (machine) is attached to a cable (think bicycle lock cable) that can be wrapped around a person (or two) and activated. Whoever is within the cable experiences normal time-flow but sees the outside world as stopped. In the story, several days are spent in this "frozen" world by the detective and the girl. The author's great descriptions of the time-frozen world are what I remember best. Finally, using the bad guy's stolen "cable" the girl returns to her father's lab and is reunited with her father. The detective arrives shortly after and the scientist offers to introduce his daughter to him but instead he walks directly to her, takes her in his arms and kisses her.
