Although we have seen from the Ran that leftover Shabbos candles don’t need to be treated the same way as leftover Chanukah candles, we don’t see that there is any heter to throw them into the garbage. All the Ran say is, one doesn’t have to burn leftover Shabbos candles the same way as Chanukah candles, however, perhaps they must still be treated with respect, and shouldn’t be thrown in the garbage.
The truth is, the Kaf HaChaim (297:11) writes, that they should be buried respectfully like tashmishay kedusha. R’ Elyashiv (sefer Ginzei Kodesh pg. 194) also held that they should be treated with respect, and he held that one should wrap up any leftovers from the Shabbos candles and only then throw it into the garbage.
However, R’ Shlomah Zalman (Shemiras Shabbos 43:44) held, since they come to give one benefit by ensuring that he doesn’t end up tripping up on wood and stone, and that one is allowed to benefit from them and carry out mundane activities in front of them, they have no kedusha, and they can simply be thrown into the garbage. Although the Shulchan Aruch (end of 275) writes that one shouldn’t undress a child in front of them, there is a difference between when they are actually burning and a mitzvah is being done with them, and afterwards, where no mitzvah is being done.
