Secondary teachers believe the new arrangements could disadvantage some pupils because it is still not clear who will pay.
The situation has arisen after the Scottish Qualifications Authority (SQA) has introduced charges for the first time to cut down on bogus appeals.
The costs range from £10 for a basic check to see if the marks have been added up correctly to £40 for a full marking review.
There will be no cost if a mistake has been made, but if the appeal is unsuccessful the charges will apply.
The SQA has said it is up to local authorities to decide whether the costs are paid from central funds or taken from school budgets.
However, the Scottish Secondary Teachers' Association (SSTA) argues leaving the decision to schools could create a postcode lottery, particularly at a time of tight budgets.
A motion to the union's annual congress on Friday calls on the Scottish Government and council umbrella body Cosla to work together to ensure "standard practice throughout Scotland thus protecting equal opportunities for all".
Alan McKenzie, the SSTA's acting general secretary, said the issue was of growing concern as this summer's deadline for appeals approached.
He said: "The problem is that there is no uniform system in operation across Scotland, and that creates a situation where young people may suffer and parents will be comparing what happens in different parts of Scotland.
"We do not want to be in the perverse situation where schools feel they cannot take a number of appeals to the SQA if they cannot afford them if they are unsuccessful."
Douglas Chapman, education spokesman for Cosla, said: "We would be delighted to meet with the SSTA at the earliest opportunity to ensure no child is disadvantaged by the changes introduced to the appeals system."
A Scottish Government spokesman said council directors of education had confirmed local authorities would meet the costs associated with the use of the new results service - although it was not stated whether that would be done through school budgets or centrally.
"Any pupil who needs it will be able to benefit from this service," the spokesman added.
An SQA spokeswoman said the body expected requests for clerical checks and marking reviews to be made only if the school or college was confident there had been an error.
The move by the SQA, announced two years ago, has been broadly welcomed, with many agreeing the old system was misused. Originally intended as a safety net for exceptional cases, in recent years appeals have become widely used for pupils who "had a bad day" in the exam.
Last year, the SQA received 67,000 requests - meaning about 7% of exam entries were appealed - but fewer than half were successful and the process cost the body almost £800,000.
However, Ken Cunningham, general secretary of headteacher body School Leaders Scotland, has already highlighted concerns over the payment of appeal charges.
"If individual schools have to pay, that could lead to inequalities in the system because some schools would be able to afford it and others would not," he said.
And Liz Smith, young people spokeswoman for the Scottish Conservatives, has previously called on the Scottish Government to issue guidance on who should pay the charges.