Connemara Mining plc, chaired by Mr Teeling, is opposing the winding-up petition brought by UK mining finance company Trampus Ltd.
Connemara says it has not failed to pay debts and also says Trampus cannot seek a winding up because it is not a creditor.
Ms Justice Mary Laffoy yesterday said she would give her decision on the petition later.
Connemara was set up in 2006 to exploit zinc and other mineral mining opportunities in Ireland. It has obtained licences for a number of locations in Ireland and one of its subsidiaries, Limerick Zinc Ltd, has attracted investment from a Canadian company, Teck, to help exploit zinc reserves covered by the licences.
Trampus is the largest single shareholder in Connemara, holding 1.625m shares, or 6.32% of the company. Mr Teeling is also a substantial shareholder.
Mr Teeling, who also has a number of other mining business interests, is the founder of whiskey producer Cooley Distillery, which was sold to an American spirits company more than a year ago for €73m.
In its petition, Trampus says Connemara’s financial position has been deteriorating and interim accounts for 2012 show it has liabilities of €363,000 compared to assets and cash of €283,000, resulting in a deficit of €80,000.
Its inability to pay its debts was shown by a notification to shareholders in November that it was immediately ceasing to make payments towards the funding of Limerick Zinc under the terms of its joint venture agreement with Teck. This was in spite of previous assurances from directors that the company had sufficient funds to meet its obligations under that agreement until 2013, Trampus said.
Mr Teeling told investors at a meeting in London last November that the cash required to be invested in Limerick Zinc would not be recouped because the value of the project was less than the present value of any additional investment, Trampus said.