Where can children go after school when both parents work?

Legislation now hovering in the Senate may help the 16 million school-age children of working parents, particularly those children - one estimate says 6 million - who go home to empty houses each day.

The bill, proposed by Sens. Donald W. Riegle Jr. (D) of Michigan and Claiborne Pell (D) of Rhode Island, is designed to aid school-age children needing supervision outside school hours.

The bill's key provisions:

* A sum of $15 million a year for three years to public agencies and private, nonprofit organizations using public school facilities for school-age child care.

* Assistance to lower-income families using these services.

* A nationwide assessment of school-age child-care needs.

A member of Senator Pell's staff, while admitting that none of the dozen cosponsors they have attracted so far are Republicans, thinks the bill has a ''good chance of passing next year.''

Michelle Seligson, director of the School-Age Child Care Project, a resource center in Wellesley, Mass., calls the bill ''a gigantic leap forward'' and views it as a model piece of legislation for states to follow.

Her group found that for at least 20 years, organizations like the YMCA, Boys and Girls Clubs, and recreation departments picked up many empty-house children on an informal basis. ''But now,'' says Ms. Seligson, ''they find that the kids are being dropped off hours before the centers open.''

With the great increase in dual-career couples and single parents, schools are having the same experience. A Midwestern principal describes what he has faced with these kids: ''A child swallowed a lollipop, stick and all, after school on his way home. There was nobody at home and he came running back to school. Kids were getting home and getting in other kids' apartments and raising all kinds of Cain.''

Principals and community leaders, together with dedicated groups of parents, are working to create before- and after-school care for the children of working parents. Ms. Seligson says there are ''no hard data on how many centers are now open.'' Her project gets about 3,000 calls for assistance each year, and she reckons that school-age child care (SACC) is now available in at least some parts of most large cities - chiefly the suburbs.

''The great need now is for some form of subsidized care for the inner-city school kids,'' she says. The project's continued efforts to help fledgling SACC groups indicate that ''the amount of school-age child care available is nowhere near adequate.''

Although programs are housed in churches, ''Y's,'' private homes, and other community shelters, most are now leasing schoolrooms. According to a school administrator in Montgomery County, Md., such arrangements ''give us a little return for the extra space available due to declining school enrollments, and keep down the wear and tear on these children by giving them one place to go all day.''

Caring for these children all day at schools, says an administrator in Arlington, Va., who pioneered this approach 11 years ago, ''pleases nearly everyone. The liberals are happy because we do educational things with the kids, the law-and-order people are happy because we keep them off the street, and the parents are happy because their kids aren't going home to an empty house.''

Some groups, however, don't share this enthusiasm. Legislators in a few states (including Virginia) have tried to preclude schools from housing such programs, saying that it encourages women to leave their children, competes unfairly with private-sector day care, and places a noneducational burden on the school.

Ms. Seligson dismisses the first argument (''Women are going to work anyway''), believes that a mix of private and nonprofit day care ''still doesn't meet the need,'' and points out that schools have been involved in day care before - ''during World War II, so the women could work in factories.''

She says that her group ''hears of very little opposition'' to the concept itself. The problems they hear about instead are organizational ones. Organization, at this point, is ''very grass roots,'' she reports. With the exception of the proposed federal School-Age Child Care bill, ''there really has been almost no federal or state support for SACC,'' she says.

For now, says Ms. Seligson, parents, principals, and others are finding their support instead in their communities. For instance, one bank in Michigan underwrote the start-up costs for a program, some Y's offer free swimming, and the League of Women Voters takes surveys to determine the needs of the community.

''There hasn't been a national needs assessment at this point,'' says Ms. Seligson, who adds that her project is just now trying to find out how many programs have been started to date. ''There have been no hard studies done on the effects of school-age child care. But there are so many variables in a child's life, it's hard to see how you would pick out the factors affected by child care.''

Parents tend to feel better about enrolling their children in these programs than letting them go home to an empty house, she points out. ''And we know that when parents feel good about what they're doing, it impacts positively on the children.'' Still, she admits, the ''content of most of these programs is not that good. We don't know what makes a good SACC program, the way we know what makes a good day-care program for younger children.''

The Wellesley project has received funding for two more years from the Carnegie Institute and the Ford Foundation to help others develop and improve such programs.

For more information, write: School-Age Child Care Project, Wellesley College Center for Research on Women, Wellesley, Mass. 02181 - (617) 235-0320, Ext. 2544 .