By Letter/In Formal Speeches

Mayor - "The Worshipful the Mayor of the Royal Borough of Windsor and Maidenhead Councillor (and thier name)" and his/her partner as "The Mayoress/Mayor's Consort (or Escort) of the Royal Borough of Windsor and Maidenhead". 

Deputy Mayor - "The Deputy Mayor of the Royal Borough of Windsor and Maidenhead Councillor (and thier name)" and his/her partner as "Deputy Mayoress/Deputy Mayor's Consort or Escort" as appropriate. 

Thereafter they may be addressed as 'Mr Mayor', 'Mayoress' or 'Mayor's Consort (or Escort)', 'Deputy Mayor' and 'Deputy Mayoress/Deputy Mayor's Consort/Escort' as appropriate.

On Invitations

The Worshipful the Mayor of the Royal Borough of Windsor and Maidenhead Councillor (and their name)
or
The Worshipful the Mayor and Mayoress/Mayor's Consort (or Escort) of the Royal Borough of Windsor and Maidenhead
Councillor (and thier name) and (and thier name).

or

The Deputy Mayor and Deputy Mayoress/Consort or Escort of the Royal Borough of Windsor and Maidenhead
Councillor (and thier name) and (and their name).

Female Mayors

In the case of a female Mayor, it is customary to address her as 'Mr Mayor', although some lady Mayors have expressed their preference for 'Madam Mayor' – people will be advised if this is the case.