Although it is seldom drunk today, it's one of the classic cocktails for a reason, and definitely something you should try.
I mixed up one in the original fashion, using Dutch genever instead of the more typical London Dry gin.
Made in this way, you can think of the Martinez as a variation on the Manhattan, since genever has a flavor that is in some ways reminiscent of a young bourbon (along with the added botanical flavors, including juniper, that are usually found in gin).
The result is on the sweet side — you could cut back on the vermouth a little to modify that, if desired — but quite delicious.
1 1/2 oz Bols Genever
1 1/2 oz Sweet Vermouth
1/4 oz Orange Curacao
2 Dashes Angostura Bitters
Stir with ice, then strain into a chilled cocktail glass.
I recommend the Bols Genever for this cocktail, although you can substitute a different genever (prefreably of the oude variety) if that's all you have.
I used Martini sweet vermouth — any good sweet vermouth would work, just make sure it's fresh.
Marie Brizard is my go-to curacao, and it's definitely worth seeking out. If you don't have orange curacao, you can substitute Grand Marnier, although you might use a little less since it's sweeter.
Edit (4/18): The original inspiration for this post was based on something I read on Difford's Guide, which claimed genever as the spirit in the original Martinez. However, it now appears that the support for that claim is tenuous at best. When I asked David Wondrich about it, he prounounced it, "Unlikely. There's a divide in the late 19th century, with Holland gin going into the old classics and English gin in the new drinks…I [don't] believe that there's such thing as a Martinez as distinct from a Martini."