For small taps, in the Mill, I use a spring loaded gadget (a Tap Tru?) to keep the tap vertical, while the tap is turned by a small tap wrench.
For larger sizes, I made some holders which convert Taper Shank Reamers to Hand Reamers. The adaptor has a centre in the end, which is steadied by a centre in the quill, while the adaptor is turned by a Tap Wrench on the square. If a hand Reamer has a centre in the end, the same technique can be used.
For reaming in the Lathe, I made a pair of Floating Reamer holders. Parallel shank Hand reamers are held in ER25 collets, whilst M T shank reamers are held in shop made ER32 collets. If anything is off centre, the "float" allows the reamer to follow the drilling, rather than behaving as a boring bar.
Howard.