The Scottish Council for Independent Schools (SCIS) data, released last week, shows that 93 per cent of S5 pupils attained at least a C at Higher, and 56 per cent of these an A grade.
This covers mainstream independent schools only, and represents the same performance as last year, which was the best for grades since 2007 when the SCIS began its analysis.
For all private schools, the overall pass rate slipped to 90.8 per cent from 91.3 per cent in 2012, whereas pass rates for all schools in Scotland have edged up to 77.4 per cent from 76.9 per cent.
Pupils at independent schools also bucked the national trend in some foreign languages, with a 12.3 per cent rise in the number of candidates taking Higher French this year, compared with a 9.6 per cent drop in all Scottish schools.
John Edward, SCIS director, said: “This year’s SQA results, combined with those at A level and the International Baccalaureate, recognise the purposeful learning environment that exists at Scotland’s independent schools. Pupils and teachers are to be congratulated for their hard work.
“At Higher and Advanced Higher level, more than 90 per cent of pupils achieved A to C passes which is a fantastic achievement, especially when you consider that most independent schools admit children of mixed abilities.
“It’s evident that our schools are keeping faith with a breadth of subjects and bucking the national trend. An important factor in pupils’ exam success is that independent schools have the freedom to offer whichever curriculum and qualifications they believe best meet the needs of their pupils.”
Although most private schools in Scotland offer Highers, some opt instead for A levels or the International Baccalaureate.
Meanwhile, more Scots would prefer to send their children to state schools than private ones even if there were no fees, according to a study released last week.
The YouGov research found 62 per cent of those questioned in Scotland preferred local authority run schools, the highest figure in the UK.