How to fix font rendering in browsers of various operating systems?

Question

Fonts

I've been struggling with the problem for a long time:
1) Some (or rather many) fonts are rendered in browsers on different operating systems (win, mac, android) in different ways and often radically differently - this causes serious problems in layout.
Usually the line "moves out" from its usual place - i.e. the character in the line height is either higher or lower than usual (on another OS)

An example of a screenshot from Android (everything is fine on a Windows desktop):

What is the right way to solve such problems? Maybe there is a set of proven fonts that render identically? Maybe some preparatory work is needed to use the font?