A manufacturer that might have devoted weeks to training a new employee to operate elaborate metal-cutting machinery now often insists that job applicants obtain certification on such machines before even applying. Some cities whose police and fire academies once had programs to train rookies now expect job applicants to attend outside schools and pay for it themselves.

“This means the employee is accepting the cost of the training before even getting considered for hiring,” said Jim Jacobs, president of Macomb Community College in Michigan. Mr. Jacobs said that credit and noncredit courses and programs were often similar and that qualifying only degree-seeking students for federal Pell grants and federal loans often seemed arbitrary. The presidents of several colleges said the lack of financial aid for certificate students hurts more than just those students. Gail O. Mellow, president of LaGuardia Community College in Queens, said the lack of aid made it hard for her college to attract and train all the students the city needs to do coding for Manhattan’s Silicon Alley or to work in its “green waste management program.”

Robert G. Templin Jr., president of Northern Virginia Community College, said the lack of financial aid had kept his institution from expanding some certificate programs that might help meet demand from employers. Dr. Templin, whose college has 20,000 continuing education students, about half pursuing certificates, mentioned in particular a program for information technology certificates, which can cost $800 to $4,000.

He said some who would like to pursue certificates have been unemployed for months or are from low-income households.

“There is a group that typically tends to be individuals who are financially very fragile,” Dr. Templin said. “For some of them, paying the tuition is often cost-prohibitive. And not having a source of reliable student aid discourages institutions like ours from offering some of these training programs for job categories that are among the fastest growing in the nation.”

Northern Virginia is offering a program for certified nurses’ aides this spring, but officials there said they were forced to delay it until April because several interested students were having problems pulling together the money needed to enroll. Some students, for the most part those who have been unemployed, can obtain federal aid for programs under the Workforce Investment Act, but many fail to, partly because there is not enough money.

Ana Bausher, scheduled to begin that four-week nursing aide program in April, said it was hard to come up with the $1,600 fee.