With high home prices, low inventory and heated bidding wars, Seattle is the new San Francisco.

In the metro Seattle area, home-sale prices rose 9.5% from 2014 to 2015, putting the median home value at $385,300, according to the National Association of Realtors. That’s below the limit for government-backed loans for the area, which currently is $540,500. But Seattle buyers who want a dream home in a desirable neighborhood will probabl0y need a jumbo mortgage.

Seattle still lags behind San Francisco, where the median home value is $781,600, but buyers in both cities—many in the tech industry—are competing for a limited pool of properties.

John O’Brien, age 37, and wife Emily, 34, and two children, ages 2 and 4, moved to Seattle from San Francisco in July and rent a four-bedroom house for $4,300 a month. They have since had another baby and are feeling the squeeze.

Before house-hunting, they submitted income and credit documentation to a lender to find out how much they could afford, says Mr. O’Brien, vice president of media strategy for the OutCast Agency, a communications and marketing firm.