The ancients could easily achieve 97- 98% in gold or silver when they wanted to, but getting over 99% seems to have proved difficult as analyses I've seen on
Republican silver (theoretically pure) only rarely seems to reach 99%. The existence of trace elements soemetimes leads to an odd consequende that the value of residual gold in almost pure silver can at times reach 0.5% and thus at times can add substantially to a coin's theoretical value although not to their practical value as one wouldn't know what specific coins might have significant residual gold traces and as the seignorage would far exceed the typical (though not the exceptional) value of trace elements that might be recovered by a more thorough smelting and separation. 98% gold is 23.5 carats and I'd say that was typical of late
Republican and early Imperial gold. I can't specifically comment on
Byzantine but I'd assume it was similar.