First of all, I love [name_m]Henry[/name_m] and [name_f]Caroline[/name_f] together! [name_m]Emerson[/name_m] is a great idea but doesn’t really seem to match your twins’ style. Maybe as a middle name? [name_m]Anderson[/name_m] could also be a great middle name for a boy!
[name_f][/name_f]For a girl (besides just using [name_f]Emily[/name_f], which could definitely work!)
[name_f][/name_f][name_f]Emma[/name_f]
[name_f][/name_f]Emilia/Amelia
[name_f][/name_f]Emilie/Amelie
[name_f][/name_f]Mille/Millie
[name_f][/name_f]Anne/Anna (for Anderson)
[name_f][/name_f]Anneliese/Annalise
[name_f][/name_f][name_f]Drea[/name_f] (feminine form of Andrew)
[name_f][/name_f][name_f]Andrea[/name_f]
[name_f][/name_f][name_f]Andrina[/name_f]
[name_f][/name_f]Any name ending in -son (although these also don’t really match [name_m]Henry[/name_m] and Caroline)
For a boy:
[name_f][/name_f][name_m]Andrew[/name_m]
[name_f][/name_f][name_m]Anders[/name_m]
[name_f][/name_f][name_m]Alexander[/name_m]
[name_f][/name_f][name_m]Emil[/name_m]
[name_f][/name_f][name_m]Drew[/name_m]
[name_f][/name_f]Andre/Andreas