This is the SACE Honour Roll, listing every award, merit or prize won by South Australian SACE students in 2004, along with their school and subject details.
The report also includes significant Australian national awards and prizes such as the Australian Student Prize.
| 454 | Hardy, Rhiannon Kate | SA | Merit | Visual Arts Studies | |
| 455 | Harley, Simon John Douglas | SA | Merit | Drama Studies | |
| 456 | Harm, Matthew David | SA | Merit | Chemistry | |
| 457 | Harm, Matthew David | SA | Merit | Physics | |
| 458 | Harper, Sophie Gibb | SA | Merit | Drama Studies | |
| 459 | Harper, Sophie Gibb | SA | Merit | English Studies | |
| 460 | Harper, Sophie Gibb | SA | Merit | Modern History | |
| 461 | Harradine, Shellee Jade | SA | Merit | Early Childhood Studies | |
| 462 | Harrison, Larissa Kaye | SA | Merit | Economics | |
| 463 | Harrison, Larissa Kaye | SA | Merit | Legal Studies | |
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| 464 | Hart, Thomas James | SA | Merit | Composing and Arranging | |
| 465 | Hartnett, Nicole Alexandra | SA | Merit | Biology | |
| 466 | Harvey, Daniel John | SA | Merit | Mathematical Studies | |
| 467 | Harvey, Jackson | SA | Merit | Biology | |
| 468 | Hasegawa, Yukiko | SA | Merit | Japanese (Continuers) | |
| 469 | Haslam, Timothy Colin | SA | Merit | Modern History | |
| 470 | Hausler, Ella Beth | SA | Merit | Community Services B | |
| 471 | Hay, Kate | SA | Merit | Physical Education | |
| 472 | Hayman, Talia | SA | Merit | Physical Education | |
| 473 | Hayman, Talia | SA | Merit | Tourism | |
| 474 | Hayter, Llian | SA | Merit | Sport and Recreation B | |
| 475 | Haywood, Laura Anne | SA | Merit | Communication Products A | |
| 476 | Hearn, Kellie Barbara | SA | Merit | The Arts and the Community | |
| 477 | Heatley, Sarah Jane | SA | Merit | Mathematical Applications | |
| 478 | Hebenstreit, Nikki Elise Stirling | SA | Merit | Biology | |
| 479 | Hebenstreit, Nikki Elise Stirling | SA | Merit | Studies of Societies | |
| 480 | Heenan, Kimberley Anne | SA | Merit | Modern History | |
| 481 | Heenan, Kimberley Anne | SA | Merit | Physics | |
| 482 | Heenan, Kimberley Anne | SA | Merit | Specialist Mathematics | |
| 483 | Heenan, Kimberley Anne | Wilderness School | Medindie | Australian Student Prize | |
| 484 | Height, Kimberley | SA | Merit | English Studies | |
| 485 | Hendry, Nicole | SA | Merit | Psychology | |
| 486 | Herczeg, Yolanda Megan | SA | Merit | Musicianship | |
| 487 | Herde, Prue | SA | Merit | Studies of Societies | |
| 488 | Herve, Alexander Edward | SA | Merit | Mathematical Studies | |
| 489 | Heuch, Fiona Jane | SA | Merit | English Studies | |
| 490 | Heuch, Fiona Jane | SA | Merit | Mathematical Studies | |
| 491 | Hill, Aaron Patrick | SA | Merit | Economics | |
| 492 | Hill, Michelle Kate | SA | Merit | Health Education | |
| 493 | Hill, Rebecca Natani | SA | Merit | Tourism | |
| 494 | Hillgrove, Kate Amelia | SA | Merit | Solo Performance | |
| 495 | Hillier, Alicia | SA | Merit | Design, Construction and the Community | |
| 496 | Hinze, Stewart William | SA | Merit | Agricultural and Horticultural Practice | |
| 497 | Hiscock-Croft, Benjamin David | SA | Merit | Chemistry | |
| 498 | Ho, Perona Pui Yui | SA | Merit | English as Second Language Studies | |
| 499 | Hodge, Stuart | SA | Merit | English Communications | |
| 500 | Hodgkin, Kylie Cherie | SA | Merit | Religions in Australia | |
| 501 | Hoffman, Simon John | SA | Merit | Mathematical Studies | |
| 502 | Hofmann-Thorpe, Ellin Rose | SA | Merit | Ensemble Performance | |
| 503 | Hollingsworth, Lucy | SA | Merit | Modern History | |