In his book, Miracles (Grand Rapids, Michigan: Baker Academic, 2011), Craig Keener cites many examples of modern miracle reports that involve the testimony of eyewitnesses, medical documentation, and other forms of evidence. Below are several examples. Much of what I'm presenting here is in summary form. Keener often provides more information than I'm going to include, such as more information about his relationship with some of the witnesses and more details about physical illnesses that were healed. Those who want fuller accounts can consult his book.
Anna Gulick had a severe problem with her sight in her right eye, a problem that improved after a "strange sensation" in the eye that followed prayer for healing (316). Keener writes that "the doctor acknowledged that there was no medical explanation for the tested, physical changes in her eye" (316). He cites the testimony he received from Gulick herself and "documentation from her doctors", one a macular degeneration specialist and the other an optometrist (n. 53 on 316-317).
Concerning another case, Keener writes:
"The fertility doctor explained that Tariku Kebede Woldeyes and his wife, Adanech Negash Tesema, who had moved to the United States, would not be able to have a pregnancy, and the medical condition is clearly documented in the material that they sent me. Pastor Dawit prayed for them, noted their specific physical problem, and declared that within a year, the wife would become pregnant. After the wife became pregnant, they returned to the fertility doctor and nurse, who confirmed that this was beyond normal natural expectations." (321)
Some other cases:
A young filmmaker teaching at the time at Judson University videotaped Heidi [Baker] and some orphans praying for a non-Christian woman known in her village to be deaf. This person's recovery of hearing, along with the healing of another person on the same trip, provides one of the more dramatic scenes in the film. One of my students, Amanda Hammill Kaminski, who had met Heidi Baker through YWAM, told me that her roommate had spent some time working with Heidi Baker and during that time witnessed numerous conspicuously visible miracles.When I was asking another contact, Shelley Hollis, about healings she had witnessed, she mentioned her experiences in Mozambique about a year and a half before our conversation. Before she raised the subject, I had not been aware that she had spent any time in Mozambique, but she independently confirmed reports about the ministry of the Bakers and their Mozambican colleagues. She said that when she was present, in one village without any Christians, Heidi asked a crowd of about a thousand if anyone was sick. A deaf and mute girl of about eight or nine came forward, and Heidi prayed; the girl began to hear first and then gradually began to try to imitate sounds whispered in her ear. Immediately, Shelley noted, the reaction swept through the crowd like a wave from front to back, from whispering to ululation and finally jumping up and down. Shelley witnessed a deaf boy about the same age healed the same night, and the next day a church was started.Shortly after this, Shelley was preaching in another village there with no Christians. A commotion started in the back while she was preaching, but she continued preaching until she discovered that in the back, a teenage girl had started to hear for the first time. The girl's mother brought her forward and began to testify that her daughter had begun to hear. While they were testifying, the blind right eye of a woman to Shelley's left was suddenly healed. Shelley announced that God was healing people and instructed them to bring the sick. In response, they brought a paralyzed woman on a mat. The woman then got up and began to dance! None of these people, Shelley emphasized, were yet Christians, although before the night was over some five hundred people committed themselves to become followers of Christ, and a church was started the next day. Presumably the locals who knew those who were cured believed that something dramatic had happened. The probability of an alternative explanation seems abysmally low: Would a village, though already committed to a particular religion, fake all these healings and then contribute so many members to a permanent new church, just to fool some visiting Christians? More recently, a research team has discovered surprising medical confirmation of claims of healings of blindness and deafness taking place there. In view of such evidence, I believe that the sorts of claims surrounding the Bakers' ministry should appear credible to those who do not presuppose that such events cannot happen. (331-332)
Here's one of many reports Keener cites from a doctor who witnessed a healing, in this case a doctor he interviewed himself (Mirtha Venero Boza):
"The hand of her baby granddaughter was severely burned by a hot iron; it was swollen and skin was peeling off. Within less than half an hour of prayer, and without medical intervention, the baby's hand was restored completely, as if it had never been burned." (345)
Keener contacted Yazmin Hommer, who had suffered from severe cerebral malaria and whose organs were beginning to fail. Her "doctor was shocked and regarded her recovery [after prayer] as astonishing." Keener continues, "Yazmin has provided me much of the copious medical documentation that attended her situation." (350)
Some of the accounts Keener cites include stories reporting on the miracle in the mainstream media. Here's an example:
"Clint Yeatts, 'Power of Prayer: Kayla Knight,' on KLTV (an ABC affiliate), July 20, 2008, reports (with MRI photos) about an eleven-year-old girl whose brain tumor covered nearly a fourth of her brain. Two days after prayer, and before any treatment could begin, an MRI showed that the tumor was gone, a result confirmed by a subsequent MRI [see here]…Dr. Nicole Matthews notes that infections can sometimes mimic tumors, but assuming the accuracy of the report, this sounds like a genuine miracle (personal correspondence, July 7, 2009)." (n. 15 on 428)