Demonstrators took to the streets in the west, the heartland of support for Odinga, who maintains he was the victor of an election that returned President Uhuru Kenyatta to power a year ago.
Two other opposition lawmakers were also arrested and later released for their involvement in the ceremony.
They were shut on Tuesday when trying to broadcast live footage of opposition leader Raila Odinga's symbolic presidential inauguration. So far police have not arrested Odinga.
Miguna has been in police custody since Friday morning when he was arrested dramatically from his Runda house, which was extensively damaged. Police said they charged Miguna in a court outside the capital, Nairobi.
He was charged with "being present and consenting to the administration of an oath to commit a capital offence, namely treason", says the charge sheet quoted by Reuters.
The lifting of the ban on the two stations comes days after the suspension of the independent TV stations was suspended by a High Court.
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"Once again the state is willfully violating Mr Miguna's rights by moving him without any notice to his lawyers or his family and, in order to frustrate their access to him, to a court stationed outside Nairobi", Isaac Okero, president of the Law Society of Kenya, told reporters.
"As soon as we serve the order this morning I expect the stations to be back on", he said.
The NASA leaders include Siaya Senator James Orengo, Mombasa Governor Hassan Joho, Vihiga Senator George Khaniri, Kakamega Senator Cleophas Malala, businessman Jimi Wanjigi, and economist David Ndii. His supporters in the opposition stronghold of Kisumu city in western Kenya clashed with police, who fired tear gas at them.
Kenyatta won the August election, and won the repeat election in October as well after Odinga boycotted it, complaining it would not be fair.
The government took three private television channels off the air on Tuesday as they began to cover of the opposition ceremony.
The Committee to Protect Journalists (CPJ) said government's refusal to abide by court orders was contempt for the rule of law and a brazen example of censorship.