Waiving an appraisal is a high risk move and I wouldn't do it unless I had a really clear idea on the value of the home. This is more directed to agents representing home buyers because they are ultimately going to be responsible for paying the difference in case the home appraises at a lower value then what was agreed on in the contract. Do your due diligence and amass as many comps as you can that will justify that the value of the home is as close to on par as it can be to the amount that your buyer is willing to offer. If not, this could really come back and bite you in the rear.
For example, a home is listed at $315K, a buyer offers $330K and that offer gets accepted. The Listing Agent, at some point during the process (preferably before the buyer's offer gets accepted) would have informed the Selling Agent that his buyer needs to fill out an addendum stating that they are waiving the appraisal contingency. Which just basically states that the sellers will receive no less than the agreed upon amount of $330K , regardless of what the appraisal comes back as. If the appraisal comes back and the home is "appraised" at $315K, then the buyer has to pay that extra $15K, out-of-pocket to accommodate the difference between the accepted offer price and the appraised value. The reason this can be high risk is because of the potential situation that a home appraises at a much lower value, for this example, we'll say something like around $275K. In that case, the buyer would be responsible for the $55K difference. There are certainly some workarounds, but it will usually come down to more money that your buyer will need to come up with to purchase the home and as a buyer's agent you are obligated to try and limit that as much as possible.
If you are very familiar with the value of the home and have a great idea of what it will appraise for, then you don't have much to worry about, this is where the due diligence comes into play. In the situation that I had, the home appraised at $350K, which was right around where I expected it to, so everything was fine and my client ended up with $20K in equity right when they moved in. But I can't stress how important it is that you know the surrounding areas and know your comps.