Quoted the client fewer hours than it actually took...

What do you do if you quote far less than the time the job actually took?
We've all been there - you can be sure it's going to take 6 hours, but really it took 12.  
Or worse.
You're sure it's going to take 6 months but really it took 12.  

If you charge for your time, in effect you're covered.  

You say to the client I know we agreed £50/hour and it would take about 6, but we've hit the 6 hour mark and I'm nowhere near finished.  The client is annoyed, but needs the work doing.  And in the end pays twice as much as they were originally expecting.  

Or maybe you offered a fixed price estimate.  I think it's going to take 6 hours, so at my standard rate of £50/hour, that's £300.  When it takes 12 hours, that just means I actually charged £25/hour.  

One's bad for the client, the other's bad for you.  

Because in both cases, you're selling your time.  

You could go value-based.  You need to get this many extra enquiries per month, because you reckon it will give you a monthly sales boost of £5000.  So I'm going to charge you £10000 - equivalent to 2 months of that boost.  Then you don't care that if it takes 6 hours or 12 - but you do need to make sure that it really does bring in extra enquiries.  

Or you could go fixed price.  What you've asked for is slightly different, but I know from experience that this standard package will get you the same results.  It's £2000 and, because it's a standard package, I know for a fact that it only takes me 4 hours to deliver.  

Because ultimately, the client isn't buying your time.  They don't even care about your time.  

What they really want are results.  And that's really what you're selling.