There are few boards with native lithium battery support but it would be nice to add UPS like function to any 5V powered board, be it ARM or Atmel. AXP209 is integrated on some boards and I believe it would be very interesting to have it on a breakout board similar with a solar charge controller. The simplest configuration would have only 6 pins (5V--In&GND / Batt+&Batt- / 5V-Out&GND). Some extra feature would make it even better: an EN pin that would cut-off both battery and Vin input. An AO pin to measure the battery voltage, a DO to send a battery low signal (whenever the analog inputs are unavailable). Or even better, have an I2C interface that would send various readings to the SBC (input current and voltage, output current and voltage, battery voltage, IC temperature and any other geeky stuff that you can think of). Also some exposed PCB solder points should be available to configure the battery protection specs. Most of basic battery protection circuits cuts down the power when the battery voltage reaches 2.5V but this is way too low compared to the vendor's recommended value. Having the option to set the overdischarge voltage protection at 3V would be great in order to protect the batteries.
Adafruit's Powerboost 1000C does the basic functions but it's quite expensive and fairly large. A smaller (PCB and breadboard friendly to be used with flat LiPo as well as 18650 PCB mounted batts) and cheaper alternative would be great. And a deluxe version with all those extra features would be even greater.