I find this an unsatisfactory answer but perhaps it will provoke someone to make a better one along similar lines. In the 2012 US presidential election, men voted (according to exit polls) 52:45 in favour of Romney over Obama, compared with the overall result of 51:47 in favour of Obama.
So if we assume the exit polls give a perfectly accurate indication of actual voting patterns, going from the whole electorate to just men turns Obama+4 into Romney+7, an 11-point swing. And if we assume that that translates into an 11-point swing in every state, that gets Romney at least these states listed on the Wikipedia page about the election as having <10% margins for Obama: Florida (1%; 29EV), Ohio (3%; 18EV), Virginia (4%; 13EV), Colorado (5%; 9EV), Pennsylvania (5%; 20EV), New Hampshire (6%; 4EV), Iowa (6%; 6EV), Nevada (7%; 6EV), Wisconsin (7%; 10EV), Minnesota (8%; 10EV), Maine-2 (9%; 1EV), Michigan (10%; 16EV). Since Obama won by 332:206 EV, a margin of 126 EV, transferring 64 EV from Obama to Romney would yield a Romney win. The actual total of the numbers above is 142.
Those italicized assumptions are pretty dubious, but it seems like there's probably enough slack to make it not matter: a uniform 5.4% swing would have got Romney the states of Florida, Ohio, Virginia, Colorado and Pennsylvania, already comfortably more than enough to win.
To do this analysis properly we'd need state-by-state exit poll data broken down by sex (which may well exist but my very cursory search didn't find it), and estimates of how accurate exit polls are (which may also exist but I confess I haven't looked), and enough effort to put those things together properly (which, as you can see, I haven't provided) -- which is why I am not altogether satisfied by this answer. It is, however, enough to convince me pretty firmly that if women's votes had been removed from the 2012 US presidential election (while somehow changing nothing else) then Romney would have won it instead of Obama.