Best chrome silver paint

Considering that Chromium Steel is a fairly modern development, well past Roman times, I’d suggest using a basic steel color, such as Testors square bottle. Perhaps mixed in with a bit of their silver for a more polished look. And then of course drybrushed silver highlights.

I like the old testors square bottle chrome.  Great stuff.  For natural metals I like alclad - airbush only though 

For a bright, shiny, chrome silver look at Molotow markers.  This is an alcohol-based ink that is very reflective.  Markers come in 1mm, 2mm, & 4mm sizes.  They are my go to source for painting landing gear oleos.   Available at Hobby lobby and Staples office supply (in my area). 

EDIT:  If you google AIRBRUSH MOLOTOW CHROME you can see some of the auto & scifi modelers airbrushing this stuff with a high gloss finish.    Amazon has 30ml refill bottles that are airbrushable without having to break into a pen.  It is sort of expensive, about a dollar per ml   But if your are seeking a dazzling chrome finish on a model part it looks better than most metalizers and is cheaper than an aftermarket vacuum deposition chrome service

I agree with stikpusher. Roman swords would not have a highly polished finish. They might polish their swords for parades, but the swords still would not look like chrome.

  You can take a look at this:https://sbg-sword-forum.forums.net/thread/6411/roman-swords