Mr Lines-Sherwood's family in West Auckland said last night that the pair had been in touch via cellphone, but only for a minute.
"I picked up and it was literally: 'Don't talk, just listen - we're okay', another few details and [the line] was out," a family member said.
"They were sitting having a cup of tea and all of a sudden told to run up the hills."
Both Ms McCrae and Mr Lines-Sherwood are unhurt but are "a little worried and scared" about the circumstances.
The government declared an emergency in the region and evacuated 20 elderly and ill tourists by helicopter from the village of Machu Picchu Pueblo near the ruins, Lima's CPN radio said. Government officials said 1954 tourists in all had been stranded in the village.
The train is the only means of transport on the last leg of the trip to the ruins from the city of Cuzco and service was suspended after the mudslides.
"Many people have run out of dollars or Peruvian soles and are begging for food or water for their children or for accommodation. Others are strewn about the floor of the train station waiting," Mexican tourist Alva Ramirez, 40, said by telephone from a hostel.
Perurail spokeswoman Soledad Caparo said train company crews were working nonstop to clear rock and mud covering the tracks, but she said flooding of the adjacent Urubamba River had slowed the cleanup.
Heavy rains have battered the Cuzco region for the past three days.
Floods and slides killed a woman and a baby and damaged stone walls at archaeological sites.
"This year is absolutely atypical," said Tourism and Foreign Commerce Minister Martin Perez. "This situation hasn't occurred in the last 15 years ... the river has never been so high."
- ADDITIONAL REPORTING: NZPA, AP