(CBS) — Sunday is the day that the law legalizing same-sex marriage takes full effect in Illinois.

More than 1,800 licenses have been issued statewide to same-sex couples in 16 Illinois counties, 1,600 of those in Cook County.

The other 86 county clerks have told the gay rights advocacy group Equality Illinois that they will be ready Monday. Those insistent on getting a June 1 license can go to the county clerks’ offices in four downstate counties: in Champaign County (Champaign), Christian County (Taylorville), Crawford County (Robinson) and Montgomery County (Hillsboro).

There will be several “first-day” ceremonies in the Chicago area.

The Windy City Times newspaper reports that three events take place at 1 p.m. Sunday: a marriage equality blessing at The Unitarian Church of Evanston , 1330 Ridge Av.; a ceremony hosted by the United Latino Pride Organization and Lambda Legal at the Chicago Urban Arts Society, 600 W. Cermak Rd; and a celebration hosted by Ald. Harry Osterman (48) at Hollywood/Osterman Beach, 5700 N. Lake Shore Dr. Unity in Chicago, 1925 W. Thome Av., in Rogers Park, will host a group wedding ceremony at 5 p.m.

Perhaps more important legally for many couples will be the ability, beginning Monday, to convert civil union certificates to certificates of marriage that will bear the date of the original civil union.

Aside from emotional reasons, Cook County Clerk Orr said there can be important tax implications for couples who now will be able to re-file tax returns from the date of their civil union forward for additional refunds.

In order to do that, both partners must appear in person at a clerk’s office in the same county in which they entered into the civil union. Orr said the change in status will be completed, and a marriage certificate issued, at no charge.

The offer is good “indefinitely,” Orr said.