Purchase Contracts: Estimation of Home Value Besides Getting an Appraisal

My question involves real estate located in the State of: NJ

I wanted to ask if there is a way to get an estimation on the value of a home, without getting an appraisal (but more accurate than using websites like redfin, zillow, etc.)?

I would like to use such a service before getting into negotiations on price, which will occur before the mortgage company's appraisal. I'm willing to pay for a service that can provide an estimation that is more accurate than free websites, without resorting to an appraisal. Not sure if such a service exists.

Thanks

Purchase Contracts: Estimation of Home Value Besides Getting an Appraisal