This site has filter sizes for all M43 lenses:
In general it's good to buy multicoated filters. There are many brands, personally I've mostly bought Hoya whose cheapest line of multicoated filters is branded "HMC".
Without multicoating the chance of image degradation increases markedly.
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|Break by Hank3152|
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|Camp by T bird|
from A Big Year - birds
|The Maasai Shepherd by cgravel|
from - African Man - (Portrait in Black and White + A Border)