| 1. Round | 01/08/1998 | Heart of Midlothian | - | Rangers FC | 2:1 | ||||
| 2. Round | 15/08/1998 | Dundee United | - | Heart of Midlothian | 0:0 | ||||
| 6. Round | 19/09/1998 | Dunfermline Athletic | - | Heart of Midlothian | 1:1 | ||||
| 7. Round | 22/09/1998 | Heart of Midlothian | - | Motherwell FC | 3:0 |  |
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| 8. Round | 25/09/1998 | Celtic FC | - | Heart of Midlothian | 1:1 | |
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| 9. Round | 03/10/1998 | Heart of Midlothian | - | St. Johnstone FC | 1:1 | |
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| 10. Round | 16/10/1998 | Rangers FC | - | Heart of Midlothian | 3:0 | ||||
| 11. Round | 23/10/1998 | Heart of Midlothian | - | Dundee United | 0:1 | ||||
| 22. Round | 29/01/1999 | Heart of Midlothian | - | Motherwell FC | 0:2 | |
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| 23. Round | 05/02/1999 | Celtic FC | - | Heart of Midlothian | 3:0 | ||||
| 25. Round | 26/02/1999 | Heart of Midlothian | - | Aberdeen FC | 0:2 |
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