As a "consultant" I usually only accept assignments within my area of expertise. Most of the time I will say to my potential clients that what they require is not in my skillset and that I can refer them to somebody else who may have the skills they require. Even after that, as an expert you cannot know everything - so there will be times that you will need to do research. But your researching ability (and problem solving skills) is what your clients are paying you for also.

My advice is to always keep your clients updated on hours spent and what you are doing. Also ask for their approval to proceed with an estimate of hours that it will take. If you are out of your depth - tell them and offer an alternative solution.

You need to know what you can deliver and then deliver, whilst communicating your progress and hours to the client regularly. Clients don't like surprises.

But what about the other side - when you do the work, get the desired solution, within budget and then the client wants to "negotiate your fees", there are two sides to every story.