Rachel Slater, 24, and Tim Newton, 27, from the Bradford area of West Yorkshire, were climbing on Ben Nevis, in the Lochaber area of the Scottish Highlands, over the weekend.
The alarm was raised on Monday afternoon when the couple were reported to be overdue in returning from the expedition.
It is believed they had been camping in a green tent behind the Charles Inglis Clark (CIC) memorial hut on the north side of the mountain.
The hunt for the pair, involving police, mountain rescue teams and search dogs, is now in its second day as fears for their safety grow.
The teams have appealed for anyone who might have seen the climbers to get in touch immediately.
Police Scotland said the Lochaber Mountain Rescue Team (MRT) was searching for the pair on Monday and returned to the area on Tuesday.
A spokesman said: “They are receiving help from the RAF Mountain Rescue Team and the Search and Rescue Dog Association.
“The terrain does not allow for any vehicles to be used so the search is carried out on foot.”
Ms Slater is an experienced climber who is well-travelled.
In a blog, she wrote: “I’ve been around rocks my whole life as my parents are very keen climbers – most of my childhood was spent scrambling around at the bottom of the cliff with the occasional easy top rope.
“In 2005 my family moved to Calgary, Canada, and in 2007 I joined a youth climbing team at my local wall and in 2008 progressed to the competitive youth team.
“We trained three times a week at 6am and competed locally and nationally throughout the winter. In the summer and school holidays I sport climbed with my family in the Rockies and Western States of America.”
She left Canada in 2009 to study at the University of Manchester, from where she graduated with a BSc (Hons) in environmental science.
In September 2013, she completed a six-month contract with an environmental consultancy in Glasgow before embarking on a three-month sport climbing trip to France and Spain.
After returning again to Spain on her own to climb in Catalonia, she “joined the grown up world of 9-5” at the start of last year, according to her online posts.
She is currently employed as a mineral, waste and environmental consultant near Bradford. Her firm, the Mineral Planning Group, has not commented on the search.
Mr Newton, originally from Leicester, also lives in Bradford and has studied physics at the universities of Manchester and Leeds, according to his Facebook profile.
Logbook entries for Ms Slater on UKClimbing.com suggest she has conducted a number of climbs with Mr Newton.
Meanwhile, numerous messages have been posted on social media from people sharing information and voicing hope that the couple will be found safe.
The Lochaber MRT has posted a request for information on its Facebook page.
Responding to the message, Tony Walker wrote: “The missing persons are Rachel Slater (my niece) and her partner Tim Newton.
“Both very experienced climbers. Most likely they are wearing the same clothing as in the photo. Any info greatly appreciated.”
On a climbing forum, Patrick Roman said he saw the pair at the weekend.
Writing on the forum, he said: “I was outside the CIC on Saturday morning. There were two people matching the image in the photo. He was wearing a red jacket and she a green and turquoise jacket.”
The search is being carried out days after Lochaber MRT warned about the conditions on the mountain.
In a Facebook posting on Friday, the team wrote: “Stunningly beautiful today on the Ben, however extremely challenging snow conditions.”
Anyone who was climbing or walking in the Ben Nevis area over the weekend and saw the couple is being urged to contact police on 101.
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