Examine the microcassette closely to determine whether the broken ends of the tape are accessible or if they have rolled up into the tape housing. If the tape ends are inside the cassette, carefully remove the screws holding the cassette together by using the jeweler's screwdriver. (Proceed to Step 5 if the broken ends are outside the tape housing.)
Lift and remove the top half of the microcassette from the bottom half. Be sure to keep the cassette completely horizontal (flat) while doing so, so the inner components do not fall out. Set the top half aside.
Find both broken ends of the tape and pull them through the bottom of the cassette housing until several inches of broken tape are on the outside of the cassette at both broken ends. Keep the tape moving in along the same path it would as if it were still intact. Be sure the tape does not twist during this process.
Replace the top half of the microcassette. Replace the screws using the jeweler's screwdriver. Keep the microcassette horizontal during this step.
Examine the broken tape ends. If the tape appears "chewed" and has tiny holes or tears in it, you may cut the damaged part away using the craft knife.
Align the broken ends of the tape, being sure to keep the tape straight and untwisted. Tear a small piece of tape that's at least twice as wide as the microcassette tape. Press this onto the joined tape ends, smoothing it down. If desired, apply another piece of tape on the other side of the microcassette tape in the same way, so one piece of gift tape adheres to the sticky side of the other piece of gift tape.
Lay the spliced microcassette tape flat on the table. Cut and remove the excess gift tape using your craft knife. Be careful not to cut the microcassette tape.
Wind the microcassette tape back into the housing using the tip of your craft knife. Be sure the tape doesn't twist during this process.