The El Presidente has nebulous origins, but thankfully historians Anistatia Miller and Jared Brown have at least narrowed it down in their book Cuban Cocktails.
The drink is credited to German bartender Eddie Woelke, who was working in Havana, Cuba. He may or may not have invented it, but it is believed he refined it sometime between 1913 and 1921. The drink was likely named for president General Mario Garcia Menocal y Deop, and later became a favorite of the next president, Gerardo Machado. But the drink changed slightly from one president to the next.
The first version was equal parts rum and French (dry, white) vermouth, with a dash of grenadine. Machado's version (it was called Presidente Machado in one book) also had a dash of orange curacao.
In modern times, you'll see this drink made with either grenadine or curacao or both. However you decide to make it, use a real grenadine (from real pomegranate) or a good brand of curacao (instead of a ten-dollar bottle of triple sec), or both. Plus, a robust but not very dark rum.
I asked Tim Stookey, a bartender at the Presidio Social Club in San Francisco, how he makes his version that's on the menu at the restaurant. He uses a quality aged rum, an excellent vermouth, and one of the better curacaos. I guess I shouldn't be surprised.
As made by Tim Stookey at the Presidio Social Club, San Francisco
1.5 fl. oz. El Dorado 5yr Rum
.75 fl. oz. Dolin Blanco Vermouth
.5 fl. oz. Gabriel Boudier De Dijon Curacao
Stir and strain into a cocktail glass. Garnish with a brandied cherry and a squeezed orange peel.