The Swedish soprano is the outstanding Isolde and Brünnhilde of her generation and, in July, will sing the latter role in the first-ever complete Ring cycle at the Proms. Here, she reveals how she climbed the Wagnerian mountain

Nina Stemme is one of those artists who, if you are having difficulty submitting yourself to the multiple absurdities of opera, makes you believe in the artform afresh. I am jetlagged when I see the Swedish soprano in Tristan und Isolde at the Houston Grand Opera, but she is riveting, that concluding Liebestod thrilling and transcendent. In July she will sing Brünnhilde in the first-ever complete Ring cycle at the Proms, conducted by Daniel Barenboim. Kill for a ticket.

We meet the morning after her performance, in the plush, gated apartment block that is her temporary home. She is the least diva-ish diva imaginable – fetches me a coffee, talks for two hours when we had agreed one, seems to forgive me when I keep getting facts about her career wrong. As the outstanding Isolde and now Brünnhilde of her generation – she has already conquered the US in the latter role and this month sings her first complete European Ring in Vienna – she could swagger and drip with jewellery. In fact, she is friendly, approachable and wearing a sensible linen dress.

"One of my daughters calls me a diva at home sometimes," she says, "and I can be one on stage if I have to be. That's enough for me. Divas have a reputation for being quite complicated, and we can't really afford that in our operatic world. I want this artform to develop."

Stemme tells me she is exhausted but still full of adrenalin after the previous day's performance. She makes the epic role of Isolde look straightforward, but don't be deceived. "It has taken 10 years to get there," she says. "My aim is to make it seem effortless. You learn how to tackle these parts. At the moment it feels, knock on wood, almost easy. Almost. Though you still wonder what you bring across the pit to the audience. I am never sure, never secure. I am always questioning myself – could it be better? Yes, it could. All it can get is better for each performance, even if it's a tiny detail."

She is 50 this month and at her peak as a dramatic soprano. Before 2000 she had performed mainly lyric roles, but she then sang Senta in The Flying Dutchman at the Metropolitan Opera in New York, and was surprised by the results. "I thought Senta was on the limits of what I could sing, but with that production my voice developed and it has kept on developing."

Three years later she triumphed as Isolde at Glyndebourne, giving a performance the Guardian's Tim Ashley described as "ravishing". "An Isolde can be sung by a lyric dramatic soprano," she says, "and that's exactly what I was at that time," adding that Glyndebourne was perfect because it was a relatively small house with a very good orchestra. Bad orchestras, she explains, tend to overcompensate by playing too loud, and you have to fight against them. "I didn't have a typical big dramatic voice then, but my voice grew a couple of years after that."

The performance, as she readily admits, put her on the map. "I wasn't a nobody anymore. You sing your first Isolde, it goes fairly well, then everybody knows of you. That was something new I had to cope with."

She was surprised by the way her voice changed to meet the demands of this new territory. "I promised myself always to be happy with whatever repertoire I would be singing," she says, "and I really enjoyed the lyric repertoire. But I also noticed when I listened to recordings, 'Wow, the dramatic parts sound easier than the lyric parts.' I was warned by so many people, 'Don't go there, you will destroy your voice,' but here I am and I don't feel this. I go very much by my intuition, and I just said to myself, 'You should do this, Nina, and you see what happens. I think you will learn something'."

Brünnhilde, which Stemme first sang in 2008, is the ultimate test for the dramatic soprano – or, rather, the ultimate three tests, because Wagner presents a different Brünnhilde in each of the operas in which she appears. "In Walküre I think of her like Pippi Longstocking," says Stemme. "Those first hojotohos are full of happiness. She has the status of a goddess, and I assume she hasn't encountered any problems in her life before."

Brünnhilde in Die Walküre has to have both innocence and dramatic intensity. In Siegfried, cast out by her father Wotan, she is no longer a goddess but a woman who discovers the meaning of love when she meets Siegfried. This is the most lyrical of the three Brünnhildes. Indeed, the end of Siegfried is Tristan-like in the passion of the love duet.

Then, in Götterdämmerung, Brünnhilde becomes the agent of vengeance when she discovers Siegfried has betrayed her. "Her rage is terrible," says Stemme. "The singing is just crazy – high, sustained, dramatic, forceful. You don't have much left, but then you have to do the immolation scene and sound like you're as fresh as a daisy." Because of its length and the fact that it is produced less than, say, Die Walküre as a standalone opera, Götterdämmerung is the acid test for any Brünnhilde.

Stemme as Brunnhilde during a rehearsal of Wagner's Die Walkure in San Francisco. Photograph: Lea Suzuki/San Francisco Chronicle/Corbis

But Stemme is ready. She enjoyed great success in the Ring in San Francisco in 2011; has been doing the individual operas with Franz Welser-Möst in Vienna, where she is about to do a complete cycle; and in July will give the Ring in concert form with Barenboim at the Proms to mark Wagner's bicentenary. She was also invited to sing Brünnhilde in the new anniversary Ring at Bayreuth this summer, but had to turn it down because of other commitments. The invitation came five years ago but she was already booked, such is the degree of planning in a successful opera singer's schedule.

She had been careful not to book too many Brünnhildes, wondering how she would take to the part, but now regrets that there are relatively few Rings in her diary. Future invitations will be for 2018 at the earliest, and by then her voice may be past its best. "This is the problem singers face," she says. "What do I do with this five years' planning ahead of me? It doesn't leave a lot of flexibility."

Stemme's down-to-earth approach is evidenced by the degree in business and economics she completed before becoming a professional singer ("I was playing safe," she says), and by her successful juggling of career and family – she and her Swedish set-designer husband have three children. Her motto has always been "hurry slowly", working as much as possible in Europe to be close to her family, not taking on too many engagements and choosing productions carefully. "I realised early on that one yes too many could be fatal to your career," she says. "One no too many very rarely will be."

Does she worry that as she enters her 50s the voice might start to fray? "I think about it a lot," she says, "but it doesn't worry me. After 50 this is a natural process. I do my best and hope the body still copes. I will keep singing and keep asking when it's time to stop. I don't want to go on too long. Maybe I have learned something from singing the part of the Marschallin [in Richard Strauss's Der Rosenkavalier]: to go on with life as it comes, and not try to hold on to everything."

• Proms tickets are on sale from 11 May, Stemme performs on 23, 26 and 28 July. The Ring cycle at the Vienna State Opera begins on 12 May.