Something like '*saima-' (nectar/honey) in Proto-Germanic, which became 'Seim' (syrup, apparently fallen into disuse in favour of 'Sirup', which is actually an Arabic loanword) in High German, or 'zeem' (honey) in West-Flemish.
According to Häkkinen, in Finnish literary language "sima" was first mentioned in the proverbs of Henrik Florinus in 1702. In Karelian poetry its meaning is "mesi", while in Estonian dialects it means "plant juice, liquid, mucus, sweat". The Danish dialect word 'sime' ('drizzle, drip') is assumed to be of the same Germanic ancestry(?) as the Finnish word 'sima'. In German, there is also the word "Seim" for 'honey, a sticky liquid', but at least for the time being by using reconstructions it hasn't been found to connect to the word 'sima' in Finnish.