A few enemy tears are just fine in a gin martini, either directly or as an olive brine additive.

Tequila shots. Lick their salty tears off their cheeks, down a shot of tequila, suck on a lime, then throw the lime peel at them and walk away triumphantly.

Classic martini, dirty, with an olive.

Dirty martini

I would dry them on the rim of a glass for margaritas or similar

for margarita (and some other drinks) the glass rim is covered with salt. So, you could evaporate the tears and put the residue on the rim in place of salt.

Tearquila Sunrise

I think the slight saltiness would work well with coconut juice. So, would probably pair well with a pina colada.

a bloody Mary would work wee methinks

A little saltiness would taste nice in a bloody mary.

I think Dave Arnold suggests putting saline in most cocktails