Normally, your Westie pup's ears will stand up within 8 - 12 weeks, although it may rarely take up to six months for the cartilage to become strong enough to hold the ears up. Several years ago we had a Westie whose ears did not stand until she was 6 months of age. This is rare. During this time, teething uses up most of the cartilage. Keeping hair trimmed as closely as possible on the ears will help the ears stand. It is amazing how this little weight can deter the ears from standing. Take your scissors and trim closely the hair on the front and back of the ear. This usually does the trick! By 4 months, if this doesn't solve the matter, you should tape the ears.
Parker's ears stood up at 10 weeks, but after two weeks, they both flopped. We think the cartilage was injured from continuous rough play between the pups as well as the big dogs. We had to separate him from Paris and the big dogs momentarily, except for several daily visits. We have his picture (http://www.downsouthwesties.com/floppy_ears.htm) in case you ever have a problem with a pup. I would suggest you buy a roll of tape from your vet. That way, you will have the right kind of tape and the cost is usually around $3. Parker's ears were taped for two weeks. His ears turned out great. After about two weeks, you can clip the tape in a couple of places and then remove the tape by pulling it upwards so the ear is not bent.
Over the years, we have had only one pup whose ears did not stand. I occasionally suggested to the owner that they tape the ears, but they said they didn't care since it gave her 'character'.
INSTRUCTIONS: Cut the hair inside and outside of the ear VERY short. Cut a piece of tape about 4 inches long. Place the middle of the strip of tape horizontal across the inside of the puppy's ear about 1/3 of the way down from the tip of the ear. Bring the ends of the tape around to the front of the ear crossing over each other in the front of the ear going down toward the ear opening. Press the tape tight to the ear and cut off any that sticks down in the ear itself that would tickle the pup's ear. Leave the tape on for at least two weeks. Replace it if the puppy works it off. Replace it even if the ear is up. It must be on long enough for the bent cartilage of the ear to grow straight. Two weeks should be enough. The taping may need to be repeated several times. When you do take the tape off, the ear may be rather funny shaped because of the dents the tape has created in the side of the ear. This will straighten itself out in a short time.
Another way is to get a super duty brown paper grocery bag from the grocery store. Cut out a slightly rounded triangle that will just fit the inside of the ear and extend down slightly into the ear for support. For best fit, shave all the hair from the inside of the ear and for best support, shave all the hair from the top backside of the ear. Round or flex the paper into a shape that will fit the curve of the inside of the ear. Apply false eyelash glue to the paper. Be careful not to put too much on as it may ooze out from the sides, but be sure to cover the edges. Push the glued side of the paper onto the inside of the ear (apply even pressure to all areas of the ear, especially the edges) and hold it until it sticks. The paper will naturally peel away from the ear within two weeks and the ear should stand. Keep water away from the ear during this process. Do not remove the paper prematurely; you may damage the skin inside the ear. You may need to repeat this process if the ear tissue is not thick or the cartilage is not strong enough during the first application period. When the paper peels off there will be a residue inside the ear from the glue. To remove this residue, shave the inside of the ear, as the residue should be attached to the hair that is re-growing in the previously shaved area.
Our vet has also recommended giving a daily teaspoon of Knox Gelatin for about two weeks. You can mix it with his food.