For 300 ml there are measuring cups that have a scale on the side. Same for 250 ml by the way. Incidentally, I wouldn't be sure I could actually measure 1⅕ cups of anything (under your assumption that a cup is exactly 250 ml (Do I fill them completely? One cm below the top? And while about 50 % of the cups here seem to roughly fit that size, the others are different.)).

I don't order beer at all, but around here it's usually ordered as 500 ml (a little further south, especially around October, they tend to order 1 liter).