It also backed plans for women priests in dioceses where the bishop is opposed to women's ordination to be ordained and licensed by bishops outside.
This will be passed in advance of the legislation to make women priests, which cleared its last serious parliamentary hurdle on Monday and will become law in February next year.
The Archbishop of York, Dr John Habgood, told Synod: 'There has been much loose talk about cobbling together compromises, fudging the issues . . . (but) there are real and proper tensions in theology which may have to be really and properly reflected in Church life. The Church of England would be immeasurably impoverished if what those of us who sit in the middle refer to as extreme positions were to fall off.'
However, he warned that any attempt to enshrine opponents' rights in legislation would be divisive and time-consuming. All that opponents of women priests are now fighting for is that the 'flying bishops' should be full members of the Church's House of Bishops, with voting rights, and not just ordinary suffragans.
Not all the opposition came from Anglo-Catholics. Prebendary John Pearce, of London, representing conservative Evangelicals, said: 'Many of us do not need time to get used to the idea of women presbyters. The theological and scriptural objections to women in headship will remain to the end. The issue that concerns me and the 300 clergy I represent is whether there will be a place for us in 20 years time . . . We do not ask you to consider that you might be mistaken, but to have mercy on those you have defeated.'
Dr Phillip Crowe, the principal of Salisbury and Wells theological college, compared the ordination of women priests to the introduction of married priests in the 16th century. That too, he said, had been so controversial that Archbishop Thomas Cranmer had had to conceal his wife inside Lambeth Palace. But inside a generation, the reform had been fully accepted.
'Is it wise to create so much space for opponents that we end up with a yawning chasm where a church should be?' Dr Crowe asked. But he did not seriously argue against the compromise, concluding: 'If God is to be found in muddle, then in this act of Synod we may be very close to God indeed.'