Best way to interface 3v DS1337 with 5v Arduino?

So, I'm working on a clock project that uses the DS1337 (simply because I have one on hand). What I need to know is is there any way to power the DS1337 off of the arduino's 5 volts when the arduino has power and off the <3 volts of the backup battery when the arduino loses power? Would putting diodes in between the + terminals of the two voltage supplies and the RTC VCC allow the arduino to power the device when it's on and the battery to power it the rest of the time? My biggest concern is blowing up the lithium battery, my second biggest concern is the arduino leeching power off the lithium cell...
Thanks!

edit:
Also, as an alternative, I could just run the RTC off a 2200uf cap (from a guitar amp, in case they use high-self-discharge caps or something) that would get charged up when the arduino turns on. How long do you think this would this last? I calculated a decent amount of time (a few hours IIRC) a while ago but I don't really do capacitor math that much, so if anyone could confirm...

You should be able to power the DS1337 from 2 sources with low reverse current Schottky's between Vcc pin and the 2 sources. Can't see any big problems there. I use the DS1307 to avoid this exact problem - ie the Vbat pin!

Cheers,

Thanks pocketscience-unfortunately, all my schottkies are for high-voltage applications and are not suitable for these small projects. However, I do have plenty of small signal diodes with drops around .55v, would these be suitable here?

Hard to comment specifically without knowing exactly what you have, but the ones I had in mind (BAT85 or equiv) are cheap, even if you're only buying a couple of em...

Cheers,