Is there a right to appeal against a contempt of court decision?

Yes, a person punished for the offence of contempt of court (both civil and criminal contempt) has the right to appeal in the following ways:

Punishment Passed By? Who can you appeal to? Time Limit
Single Bench of the High Court  Bench of 2 or more Judges of the same High Court 30 days1 
Bench of more than one Judge of the High Court Supreme Court 60 days.(( Section 19(4)(b), Contempt of Courts Act, 1971.))
Judicial Commissioner of a Union Territory Supreme Court 60 days.(( Section 19(4)(b), Contempt of Courts Act, 1971.)) 

The law only allows a person to appeal against the decision once. If the appeal fails, no further remedy is present under the Contempt of Courts Act, 1971.  However, the Constitution of India allows an appeal against any judgment of any court, including the High Court. This is done through a unique form of a petition, known as the ‘Special Leave Petition’.((  Article 136, Constitution of India, 1950.))  The Supreme Court has the option to decide whether or not to hear an appeal arising out of the Special Leave Petition.(( Article 136, Constitution of India, 1950.)) 

  1. Section 19(4)(a),  Contempt of Courts Act, 1971. []