First you need to establish whether you are estimating the project cost or providing a quote. They are different.
An estimate is just that - based on the current scope defined, the amount you estimate it will take in hours to complete which calculates to X amount. In an estimate both parties should understand that the final cost and hours needed for completion is a "best guess" and are not solid numbers. Estimates should be close to final numbers but they often change. Estimating is often best for projects which have some ambiguous scope definitions or areas where it is unclear what may be needed until that stage of the project is reached.
A quote indicates that, based upon agreed scope, the cost for the project will be X. No guess work, no estimating. Quotes state "this is what it will cost." It is agreed upon that $X is what you will charge and $X is what the client will pay. If you fail to calculate the time you need accurately, you'll need to eat any extra hours it may take. Quotes are hard numbers and should not be changed unless both parties readily agree things have surpassed project definitions. Quotes are best used when the project is clear, straight-forward, and contains no guess work.
If your client is paying you hourly, then most instances would indicate an estimate and not a quote. Hourly pay is generally reserved for estimates because you guessed at the initial negotiations, therefore the client needs to see how much time things are taking and how close you are to the predefined estimate.
Pay for quotes isn't traditionally something which is done hourly. In many cases an upfront deposit is paid, then possibly a middle 1/3 payment, then a payment upon completion. The client isn't kept abreast of how many hours the project is taking because they've already agreed upon a flat quoted fee and that's what they expect to pay regardless of whether the project takes 5 hours or 50 hours. It's your job to calculate your time accurately when providing a quote.
In short, you need to negotiate with your client as to what payment structure best suits both of you. There's no right or wrong way to do this. It's all a matter of agreement between you.
