One of the meanings of "sphere" is planet or star, as in the phrase the music of the spheres. "High-mated" is less easy to parse, but the context provides a few connotations:
- Mated with things that are high, such as the planets or stars
- Mated with a lofty partner, one admired and high in status
- Mated in a high-minded way, not merely lustfully.
In his comment to this answer, Gareth Rees has identified earlier uses of "high-mated" that reinforce these latter two senses. The first sense, of a mate who is literally from high in the sky, would also be pertinent to Naidu. To her Indian readers, a bride mated with a celestial body would bring to mind Pandu's wives in the Mahabharata, who bore children by the sun god and a pair of twin stars.
Pandu was cursed to die if he ever engaged in sexual intercourse, but his elder wife Kunti knew an invocation that would lead the invoked deity to beget a son on her. A sage who had foreseen that she would marry a man unable to give her children had taught her this invocation. Prior to her marriage to Pandu, she had tested its efficacy on Surya, the sun god, and had given birth to Karna. When she became aware of the curse, she told Pandu about the invocation, and he advised her to beget further sons on other deities.
The gods Kunti chose as fathers of her other sons were not planets or stars. But at Pandu's urging, she shared the invocation with her younger co-wife Madri, with the stipulation that Madri could use it only once. Being no fool, Madri used her one go to invoke the Ashwins, twin sons of Surya who are associated with the stars β and γ Arietis. The twins fathered upon Madri the twins Nakula and Sahadeva.
The term "high-mated" is apt, because Kunti's and Madri's couplings with the gods are not considered primarily carnal in nature. As having been undertaken to ensure the continuance of Pandu's line, they are considered to be in accordance with dharma or righteous living. Karna is the exception: having been born before Kunti's marriage, his birth was indeed considered illegitimate. Nevertheless, he and his nephews/step-brothers Nakula and Sahadeva are among the major heroes of the Mahabharata. They would all qualify as mythological models for the future citizens of independent India, the "new glories" that "a bride high-mated with the spheres" could beget.