Huggett co-founded and served as leader of the Amsterdam Baroque Orchestra under Ton Koopman from 1980 to 1987. She was made a Fellow of the Royal Academy of Music in 1994, and serves as professor of baroque violin at the Hochschule für Künste Bremen, Germany. She won Gramophone Awards for her recordings of Bach's Sonatas and Partitas for solo violin (1997) and Biber's violin sonatas (2002).
Huggett was Artistic Director of the Portland Baroque Orchestra from 1995 until 2021. She has also served as the director of The Hanover Band and guest director of the Arion Baroque Orchestra, Montreal; Tafelmusik, Toronto; Orchestra of the Age of Enlightenment; Los Angeles Chamber Orchestra; Philharmonia Baroque, San Francisco; Norwegian Chamber Orchestra; and Concerto Copenhagen. Huggett also worked with Christopher Hogwood at the Academy of Ancient Music; with Trevor Pinnock and the English Concert; and toured the US in concert with James Galway.
Huggett continues as Artistic Director of the Irish Baroque Orchestra and is guest director of the Seville Baroque Orchestra. She also founded the baroque Ensemble Sonnerie and Hausmusik London as a chamber ensemble which concentrates on romantic music.
Huggett's expertise in the musical and social history of the baroque era, coupled with her unique interpretation of baroque music, has made her a much sought-after resource for students of the baroque violin. She has given master classes in Banff, Dartington, Vicenza, Dublin, The Hague, Medellin and The Royal College of Music.
- Heinrich Ignaz Franz von Biber: Violin Sonatas, Nisi Dominus, Passacaglia (Sonnerie / Huggett with Thomas Guthrie)
"This is a disc that merits the attention of anybody who appreciates the highest flights of violin playing, from whatever period" The Daily Telegraph, August 2001
ASV Gramophone Award Winner 2002 (Baroque Instrumental)
5* BBC Music Magazine, October 2001
“9” rating in Repertoire Magazine (France)
BBC Music Magazine Critics' Choice - December 2001
- Heinrich Ignaz Franz von Biber: Mystery Sonatas (vol. 1)
“With the tonal sweetness of Huggett’s three violins resonating pleasingly through the many double- and multiple-stoppings and her bowing demonstrating a delicious lightness and freedom, she admirably displays her eloquent command of Biber’s sublime and richly symbolic language. Huggett’s [approach] is ravishing in its sonorities, her supporting cast adding significantly to the exotic sounds of the various scordaturas and the overall effect of her intelligent, stylish and expressive playing.” The Strad Magazine, November 2004
- Heinrich Ignaz Franz von Biber: Mystery Sonatas (vol. 2)
“Huggett's playing - on three violins - shines with ease and expression” The Times
“Huggett’s imaginative approach and lively response to detail are among the most rewarding aspects of her version of these emotionally rewarding pieces.” 5* BBC Music Magazine, December 2004
“Of all the recordings now available of Biber...this [is] by far and away the most spectacular, exuberant, colourful and downright ravishing of them all. Huggett positively revels in the virtuosity of Biber’s original...Huggett’s beautifully crafted performance of the complex and, at times, profoundly moving solo Passacaglia rounds off what is a matchless recording from every perspective.” International Record Review, Nov 2004
- Johann Sebastian Bach: Violin Concertos BWV 1041, 1042, 1052 & 1056 (Monica Huggett, Sonnerie)
“No matter how many versions of the Bach violin concertos you already own, this one is a must.” International Record Review
Vivaldi: (The four seasons inside). Il cimento dell'armonia e dell'inventione Op.8. Virgin Classics. La cetra Op.9. Virgin Classics.
- "Orchestre Baroque — direction artistique : Claire Guimond". Arionbaroque.com. Retrieved 19 March 2020.
- "Det Norske Kammerorkester". Archived from the original on 5 November 2011. Retrieved 30 April 2011.
- "Irish Baroque Orchestra | Monica Huggett (Artistic Director)". Archived from the original on 13 July 2011. Retrieved 30 April 2011.
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- "Trio sonnerie". Archived from the original on 27 May 2017. Retrieved 8 April 2012.
- "Hausmusik". Archived from the original on 1 October 2011. Retrieved 19 March 2020.
- "| the Juilliard Journal Online | Juilliard". Archived from the original on 19 May 2011. Retrieved 30 April 2011.