The Veinwave machine heats thread veins, fine, visible blood vessels which appear near the surface of the skin.
They can be caused by exposure to the sun or wind.
Many adults have some thread veins, but women are more likely to be affected.
The treatment works on veins which are less than 0.3mm in diameter.
It involves placing a very fine insulated needle alongside the vein.
A microwave current is passed through the needle, obliterating the blood vessel.
The technique means the vein can be targeted, but the skin and tissue around it can be protected.
The treatment takes around fifteen minutes, and costs just under £200.
'Unsightly'
Veinwave is available at the Methley Park Hospital, Leeds.
Gill Fearnley, the sister in charge of the plastics department at the hospital, told BBC News Online facial veins disappeared instantly with the treatment, and thread veins on the legs went within eight to 10 weeks.
She said: "Previously, patients would have been treated with sclerotherapy [where the affected vein is destroyed by injecting it with an irritant solution].
"Following that, the patient has to wear bandages for a week to 10 days, but after the Veinwave treatment, you don't and you can have showers and expose yourself to sun.
"You can actually see what you're doing, unlike sclerotherapy, which is maybe not as precise."
Plastic bag
Margaret Burrows, a theatre manager at the hospital, was one of the first to have the Veinwave treatment.
She had suffered from thread veins on around her knees, thighs and ankles for eight years, and had felt self-conscious wearing shorts and sandals in summer.
She said: "The ones around the ankles were very unsightly. They could look like a bruise, and could be very painful.
"I'd tried sclerotherapy, and it had worked, but with that, you then have to wear a pressure bandage for 10 days and you can't take it off.
"If you have a number of treatments, you have to wear a plastic bag on your whole leg if you have a shower.
"And laser treatment didn't work."
She said the Veinwave treatment was a bit prickly on bony areas of the leg but she said it had worked, though she will need further treatments to ensure the thread veins are completely gone.
Mrs Burrows added: "I certainly hope to be wearing shorts and sandals next summer."