I generally do this also – though not as systematically as I would like. I find with most wines (not Nebbiolo, not old Pinot) that even pulling the same day the sediment is manageable – particularly if I use a cradle as William suggests.
I used to use a coffee filter, but stopped because of concerns that some have raised above (though I can’t say I noticed any difference). Instead I decant to near the bottom – then for the last bit use a filter or perhaps coffee filter. But I can usually get 80 percent or more of the bottle without sediment using careful pouring.
For the record, and for those who consider filtering during winemaking essentially a crime against nature, there’s no comparison between the kind of filtering we might do at home and the gear we’d use to do it, and what even sensitive winemakers might do and the filter medium they’d employ.