Sawai is a title of honor used in India, the word having its root in Sanskrit language.
Sawai literally means a quarter over one (1+1/4) in strength and / or intelligence.
In other words it means - one and a quarter of an average man in worth.   
Holders of Sawai title [ edit ]
His Highness Shrimant Sawai Madhavrao Peshwa aka Madhu Rao II Narayan was  Peshwa of the Maratha Empire in India. He was the son of Narayanrao Peshwa and was brought to power as Peshwa by the treaty of Salbai in 1782. 
Jai Singh II of Jaipur, was given title of Sawai at the age of eleven by the Mughal Emperor, Aurangzeb in the year 1699, who had summoned him to Delhi, impressed by his wit. Later he proved to be Sawai also in warfare.   The title became hereditary for his successors used by his descendants like,  Sawai Pratap Singh; Sawai Man Singh II.
Khengarji III ruler of Cutch from 1875–1942, was given the title of Sawai by British in the year 1885 The title became hereditary for his successors used by his descendants like  Vijayaraji, Madansinhji.
Ranjor Singh ruler of Ajaigarh from 1859–1919, was given the title of Sawai Maharaja in the year 1877 at the Delhi Durbar on the occasion of the proclamation of Her Majesty as Empress of India. The title became hereditary and was used by all successive rulers of Ajaigarh. 
Pratap Singh ruler of Orchha from 1874–1930, was given the title of Sawai in his lifetime and title became hereditary for rulers of Orchha. 
Bhoja Father of Shri Devnarayan. Vipul Lodaya, resident of Thane (actually not Sawai, but Dedh)
References [ edit ]
^ a b . 1922. p. 175. Indian States: A Biographical, Historical, and Administrative Survey By Somerset Playne, R. V. Solomon, J. W. Bond, Arnold Wright
^ a b . p. 49. Untitled by Prakash Talwar
^ . p. 97. Social Sci. (History) 7 (Rev.) By Consulting Editor - KV Nandini Reddy
^ Gajrani, S. (2004-01-01). . Gyan Publishing House. History, Religion and Culture of India ISBN 9788182050624.
^ Thorpe, Showick Thorpe Edgar (2009-01-01). . Pearson Education India. The Pearson General Studies Manual 2009, 1/e ISBN 9788131721339.
^ Sarkar, Jadunath (1984, reprint 1994) A History of Jaipur, New Delhi: Orient Longman, ISBN 81-250-0333-9, p.171
^ "cutch5". www.royalark.net . Retrieved . 2016-05-07
^ "AJAIGARH". members.iinet.net.au . Retrieved . 2016-05-07
^ "ORCHHA". members.iinet.net.au . Retrieved . 2016-05-07