The warning comes after a second burglary in the space of 10 days in Auckland Road West.
The second burglary happened overnight last Saturday.
The burglars got in the front door and £300 cash along with £2,000 worth of jewellery was stolen.
The jewellery taken included long diamond earrings worth £200, a diamond bracelet with five stones worth £100, a ladies wedding band with diamonds worth £200, a men's wedding band worth £200, a ruby and diamond eternity ring worth £500 and a diamond solitaire ring worth £400.
PC David Calvert, of the burglary investigation team, said: 'This is the second burglary of this nature in the area in the past 10 days.
'I would advise residents to be mindful of their home security in the warm weather, leaving doors or windows open in unoccupied rooms is an open invitation to a burglar.'
The burglary comes after another incident in Auckland Road West overnight last Thursday when a large quantity of expensive jewellery, believed to be worth several thousand pounds, was stolen.
Anyone with information should contact PC Calvert at Southsea police station on 0845 045 45 45.
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