Well, since the tables use 10ft max depth intervals, you don't need to know your exact max depth, just come close enough to be able to intelligently choose which row on the table you're going to use. If my computer were to fail on a dive, how I would handle it would depend on the nature of the dive; if I were anywhere near NDL, or given the profile, if it was a dive in which I could expect to be near NDL, I'd do a longer safety stop. I usually do one anyways, and it absolutely has improved the way I feel after several days of diving. How I'd handle subsequent dives on the same day would also depend on the situation. If the dives were not anywhere near NDL, AND I had a reliable, trusted buddy, I'd consider consulting the tables using a best estimate of max depth/time on the dive in which the computer said bye-bye, and then do a second dive with said buddy, who would clearly understand that I was using him/her for depth info on that dive. I dive without a backup depth guage, but with a watch. That would work for me on a typical 2 tank dive, so that the computer failure did not happen on a repetitive dive, making estimates with the tables more complicated...you'd have to remember your SI to the minute, which I wouldn't. If it happened on the 2nd dive, I'd probably be through for the day, unless the dives were so shallow that the whole thing was academic.
Keep in mind this; computers vary wildly in how they compute NDL and deco requirements, and none of them are proven to be any safer than the others. Consequently, adhering strictly to a particular computer's NDL info (or it's translation into tables) is no guarantee of safety. Further, lets say that the broken computer was a suunto, and that subsequent dive behavior would have sent the computer into deco, had the diver still had a working computer. Another diver using an oceanic might do exactly the same profile and have no required deco. As such, using good, common sense dive practices like very slow ascents, good profile planning and execution, and staying hydrated, etc...probably is better insurance against DCS. One last thing; when entering into mandatory deco from NDL diving, I believe the initial required stop is always at 10-15 ft. It's only when you REALLY bust the computer's algorithm that you are required to do deeper stops. So, as an added safety precaution, an extra long safety stop mimicks what your computer would be telling you to do if it had survived the dive and you had in fact exceeded NDL by a small margin.
In short, I take the computer's calculations with a grain of salt, and instead trust my awareness of the profile and dive behavior, coupled with a nice long stop, to try to maximize my dive safety. Plus, I'm paying for the damn dives, plane ticket, hotel, etc....and I'm going to enjoy that extra 5-10 minutes underwater!