I have replaced the valve stems with new ones, but the faucet still leaks.

Hey Dave... next thing will be to remove those stems again and take a good, close look at the SEATS the washers sit against (use flashlight).

If any grooves/nicks in the seats, you will need to replace the seats... That usually requires a large allen wrench set.

But there is even more to it than that... but look at the seats and see if you can get them out... get back to us... let us know how it went.

By the way... name of faucet?

Anyway, if this helped, please RATE THIS ANSWER. Thank you.