During her prolific career, May Swenson received numerous literary awards and nominations for her poetry. Often experimental in both form and appearance, her poems earned her widespread critical acclaim. As Priscilla Long commented in the Women's Review of Books, "Swenson was a visionary poet, a prodigious observer of the fragile and miraculous natural world."
Swenson's poetry has been praised for its imagery, which is alternately precise and beguiling, and for the quality of her personal and imaginative observations. Swenson's poetry "exhibits . . . her continuing alertness to the liveliness of nature. Correspondences among all life forms pour from her work, confirming that nothing is meaningless. The universe's basic beauty and balance is the stuff and soul of her poems," observed Los Angeles Times reviewer Eloise Klein Healy.
Richard Howard emphasized in a Tri-Quarterly review that Swenson's enterprise is "to get out of herself and into those larger, warmer energies of earth, and to do so by liturgical means." Howard wrote: "When May Swenson, speaking in her thaumaturgical fashion of poetry, says that 'attention to the silence in between is the amulet that makes it work,' we are reminded, while on other occasions in her work we are reassured, that there is a kind of poetry, as there used to be a kind of love, which dares not speak its name." Thus Swenson's "orphic cadences," her "siren-songs, with their obsessive reliance on the devices of incantation," are the means by which she seeks to "discover runes, the conjurations by which she can not only apostrophize the hand, the cat and the cloud in their innominate otherness, but by which she can, in some essential and relieving way, become them, leave her own impinging selfhood in the paralyzed region where names are assigned, and assume instead the energies of natural process."
Book Week contributor Chad Walsh noted: "In most of Miss Swenson's poems the sheer thingness of things is joyfully celebrated." Walsh called her "the poet par excellence of sights and colors." Stephen Stepanchev, author of American Poetry since 1945, also thought that Swenson's "distinction is that she is able to make . . . her reader see clearly what he has merely looked at before." Stepanchev, however, is one of the few critics to find her poems less than completely effective. "Miss Swenson," he wrote, "works in a free verse that is supple but rather prosaic, despite her picturemaking efforts."
Howard, writing of Swenson's development as a poet, stated that "from the first . . . Swenson has practiced, in riddles, chants, hex-signs and a whole panoply of invented sortilege unwonted in Western poetry since the Witch of Endor brought up Samuel, the ways not only of summoning Being into her grasp, but of getting herself out of that grasp and into alien shapes, into those emblems of power most often identified with the sexual." Of the more recent poems, Howard wrote: "They are the witty, resigned poems of a woman . . . eager still to manipulate the phenomenal world by magic, but so possessed, now, of the means of her identity that the ritual, spellbinding, litaneutical elements of her art, have grown consistent with her temporal, conditioned, suffering experience and seem—to pay her the highest compliment she could care to receive—no more than natural."
Reviewing Half Sun, Half Sleep; New Poems, New York Times Book Review contributor Karl Shapiro wrote: "[Swenson's] concentration on the verbal equivalent of experience is so true, so often brilliant, that one watches her with hope and pleasure, praying for victory all the way." Poetry reviewer William Stafford observed: "No one today is more deft and lucky in discovering a poem than May Swenson. Her work often appears to be proceeding calmly, just descriptive and accurate; but then suddenly it opens into something that looms beyond the material, something that impends and implies. . . . So graceful is the progression in her poems that they launch confidently into any form, carrying through it to easy, apt variations. Often her way is to define things, but the definitions have a stealthy trend; what she chooses and the way she progresses heap upon the reader a consistent, incremental effect." And Shapiro offered this analysis of Swenson's achievement in this book: "The whole volume is an album of experiments . . . that pay off. It is strange to see the once-radical carmen figuratum, the calligraphic poem, spatial forms, imagist and surreal forms—all the heritage of the early years of the century—being used with such ease and unselfconsciousness."
Swenson herself wrote that the experience of poetry is "based in a craving to get through the curtains of things as they appear, to things as they are, and then into the larger, wilder space of things as they are becoming. This ambition involves a paradox: an instinctive belief in the senses as exquisite tools for this investigation and, at the same time, a suspicion about their crudeness." Swenson also noted: "The poet, tracing the edge of a great shadow whose outline shifts and varies, proving there is an invisible moving source of light behind, hopes (naively, in view of his ephemerality) to reach and touch the foot of that solid whatever-it-is that casts the shadow. If sometimes it seems he does touch it, it is only to be faced with a more distant, even less accessible mystery. Because all is movement—all is breathing change."
Among the "strategies and devices, the shamanism and sorcery this poet deploys," as Howard admiringly described them, is Swenson's use of the riddle in Poems to Solve. The book may be enjoyed by both children and adults; the poems here are another serious attempt to accommodate "the mystery that only when a thing is apprehended as something else can it be known as itself." Swenson wrote of these poems: "It is essential, of course, with a device such as this to make not a riddle-pretending-to-be-a-poem but a poem that is also, and as if incidentally, a riddle—a solvable one. The aim is not to mystify or mislead but to clarify and make recognizable through the reader's own uncontaminated perceptions."
Nature: Poems Old and New, published four years after Swenson's death, emphasized Swenson's sympathy for and identification with the outdoors. "Swenson was an unrelentingly lyrical poet," wrote Priscilla Long in the Women's Review of Books, "a master of the poetic line in which similar sounds accumulate and resonate so that the poem exists, beyond its meanings, as a rattle or a music box, or, in moments of greatness, a symphony." Her collection Nature is "so inward, independent, and intense, so intimate and impersonal at once," wrote Yale Review critic Langdon Hammer, that "it has been difficult to place in the field of contemporary poetry." Several other critics, however, identified the work as an appreciation of Swenson's profound talent, collecting the best of her work between two covers. "The poetry thinks, feels, examines," observed a Publishers Weekly contributor; "it's patiently, meticulously sensuous, and adventurously varied in form, much as nature is." "These poems, harvested from her life's work and arranged in this delightful format," stated Rochelle Natt in the American Book Review, "promote a lasting vision of Swenson's valuable contribution to American poetry."