Natalia Doherty was last seen on 15 April 2003 in Eastbourne, where she was living at the time.
The house in Icknield Way was searched in September as part of the investigation.
Two men were later arrested and bailed in connection with the disappearance.
A Luton man, aged 66, and a 71-year-old man from Port Glasgow, Inverclyde, were detained on suspicion of assisting an offender and preventing a lawful burial.
Officers said ground survey work was now being carried out on the surface of the garden to see if the ground had been disturbed.
Detectives believe that near to the date she was last seen alive, Ms Doherty - who was also known by the surnames Wilkanowska and Logan - was thought to have travelled to Luton to stay with her ex-husband, Gerald Doherty, who has since died - at the Regents Arms in Hastings Street.
But there were no confirmed sightings of the mother-of-three in the town.
Officers from the Bedfordshire, Cambridgeshire and Hertfordshire major crime unit launched an investigation in January 2014 into the case, which has led them to believe Ms Doherty was murdered.
A police spokesman said: "Inquiries have since failed to show any sign she is alive."
Investigators are keen to trace her final movements and has asked anyone who recognises her or Mr Doherty from their time at the now-demolished pub in Hastings Street, or has any information relating to her disappearance, to contact them.

Pete Cresswell was forced to leave Liverpool University without graduating for protesting against its investments in apartheid-era South Africa.
The student was one of 10, including Channel 4 News presenter Jon Snow, punished for a six-week sit-in at the university's Senate House.
Mr Cresswell said he was "gobsmacked".
"If I went back through it 1,000 times, my 22-year-old self in 1970 would do it again," said Mr Cresswell, who was the only one of the 10 to be expelled.
The former politics student said he was "astonished" to be awarded a degree and had always thought "hell would freeze over" before the university gave him one.
Awarding him an honorary Bachelor of Arts degree at Liverpool Philharmonic Hall, vice chancellor Prof Janet Beer said "we in the university want to put this right".
She said that while the university "cannot undo" Mr Cresswell's "unfair and wrong" treatment, it can "recognise that wrong, and publicly do so" to a man who "saw what was the right thing to do and paid a price for it".
Inspired by the 1968 student revolts in France, activists across the UK brought protests and sit-ins to universities into the early 1970s and students in Liverpool were no exception.
The chancellor of the university at the time was Lord Salisbury, a known supporter of apartheid.
Mr Cresswell said: "Looking back, I think we were right and if you look at the issues, we have been proved right.
"This does put a full stop on the whole thing and I just feel pleased that a bit of history has been reviewed and put to bed."
The Birmingham-born student stayed in Liverpool and despite having to leave his politics course during his third year with a "CV from hell", eventually became a social worker, holding roles with the council and the Care Quality Commission.
Now retired, Mr Cresswell said he was pleased his daughter had had the chance to see him in robes - she graduated herself more than 10 years before him.
Mr Snow, who received an honorary degree from the university in 2011, sent him a congratulatory video message, saying: "Well done Pete. Well done Liverpool - I still love you."
Mr Cresswell said that while Mr Snow could not attend, he was "there in spirit".
A garden at a property in Luton is being examined by officers investigating the disappearance of a 50-year-old woman police now believe was murdered.
[NEXT_CONCEPT]
A student who was expelled from university for taking part in anti-apartheid demonstrations in 1970 has been awarded an honorary degree.