2004 Honda Accord vibration at 60 mph and up

2004 Honda Accord mileage: 34,000. There is a vibration from about 60 mph on up. The radial tires were rotated and balanced recently, after which I had them re-balanced and they found one tire out by one ounce. It helped reduce the vibration, but not eliminate it. They said the tires looked good with no cupping or uneven wear. How can I be assured a good balancing job was done or how do I find a place that can perform the best balancing?