The following are some of the grants, honors, and fellowships that June has been awarded.
 | North Carolina Arts Council Touring/Teaching Artist, 2005-2007 |
| Tennessee Williams Scholar, Sewanee Writers' Conference, 2004 |
| Tennessee Williams Scholar, Sewanee Writers' Conference, 2004 |
| Regional Artist Project Grant, United Arts Council, 2004 |
| Pinter Review Prize for Drama, Silver Medal, 2003 |
| Southern Appalachian Repertory Theatre National New Plays Contest Winner, 2001-2002 |
| North Carolina Arts Council Literature Fellowship, 2001-2002 |
| North Carolina Regional Artist Hub Grant, 2001 |
| Mid-Atlantic Arts Foundation: America Creates for the Millennium Finalist, 1999-2000 |
| National Endowment for the Arts New Forms Grant, 1989-1990 |
| North Carolina Arts Council Interdisciplinary Grant, 1989-1990 |
| North Carolina Humanities Council Grant, 1990 |
| Writer-in-Residence, Weymouth Center, 1990-1991 |
| Robeson County Arts Council "Distinguished Artist" Award, 1990 |
| City College of New York, Theatre Department Fellowship, 1983-1986 |
| Canadian Embassy Award, 1985 |
| James E. Gordon Bennett Memorial Scholarship, 1976 |