If you don't think that your buyers are looking at homes priced at more than they're approved for, then you're wrong. With the way the current market is, you should be too (within reason). Not everything is selling right now with multiple offers and over asking. Are you looking out for your clients and keeping tabs on price adjustments? There may be a surprise opportunity for your buyers. Homes that may not have been in their budget could be at any time. Have an accurate gauge on your buyers and the market they're looking in.
You also need to be able to adjust your strategy and communicate that clearly to your buyer. If your buyer has a budget of $500,000 then right now you might need to monitor homes up to $525,000 or even $550,000. But if that same buyer is looking in the summer at the height of the market, then you might not even show them homes priced at $500,000. You may cap at $475,000 or $450,000 because of how competitive the market will be at that time.
A good place to start is to take your buyer through a journey in the MLS before you even start looking. Look at the homes that have sold in their target area in the last year that would have met their non-negotiable list. What were they listed at and what did they sell for? Would your buyer have paid for that price? This exercise will back up what you're telling them about the current market and give you credibility. Ultimately, they will have more realistic expectations going into their search.
How do you handle the objection: "I don't want to overpay for a home?" A home is worth what the market is willing to pay for it. If a home has multiple offers over asking, then the market has determined that that home is worth that amount. There is no such thing as overpaying.