1. Use a UPS to avoid the problem in the first place

2. If failed, remove part and measure in mm from base how much it printed

3. Use netfab to split the original approximately where it failed, maybe 1 mm less than what was printed

4. Print the upper part

5. Sand and glue

You can also use the functionality from Simplify3D to start at a specific layer/height, I think, but never tried it. Yet. I installed the UPS and that eliminated the problem so far.

Cura and other slicers give output like this...

;LAYER:28
G1 F1800 E2465.10055
G1 F3000 X80.509 Y92.024 Z11.500
;TYPE:FILL
G1 F1800 E2469.60055

As you can see, it tells you which layer it's on and which "part" of the print it is working on. If you counted up and found you were on the 28th layer of your print and printing the fill, it's possible you could finish the print in theory. But the better option would be to use a 3D program or even any of the slicers that have the feature (Cura does for instance) to print just the "top half" of your print and then sand and glue it together with the part you have already printed.

Slic3r can cut a model into parts, Cura can "sink" it into the build plate so you just print half of it, or there are multiple free options that can cut your model at a specific height and then you can print it with XYZware. All of these and using acetone slurry or your favorite glue are much simpler than attempting to restart a print at a specific point.