I've interviewed for multiple positions throughout my career, I've interviewed others for software engineer positions. I've also interviewed candidates for leadership positions - in profit & non-profit organizations. These are my ideas on recruiting (specifically in tech - but some of these could apply to non-tech positions as well)... 

Recruiting for an organization is very critical skill - and having a great "recruiting team" is necessary to help build and maintain the culture of the organization. Every time there is an open position, it's an opportunity to bring in someone - the "right" someone - that can make a huge impact on an organization's goals. Here are some tips that can be incorporated to help make your process "bias-free".

• Appropriate job descriptions: The job descriptions should accurately reflect the position, should have a gender neutral tone (for example...avoid words like "javascript ninja"), and should mention benefits that would appeal to a "diverse" group - for example, 401k matching, flex time, and so on.
• Blind resume reviews: This is the practice of removing "personally identifiable information" - such as an indicator of age, gender, or race from the resume before hiring managers/decision makers review the resume and decide to call the candidate in for an interview.
• Do away with "phone screens": Many hiring managers may choose to do an "initial phone screen" to decide whether to bring the candidate in for an interview. This filters out potential candidates - especially if only one person is conducting the phone screen. If we must do a phone screen - the phone screen panel should be "diverse", to make sure there is more than one opinion on each candidate before a go/no-go decision is made.
• "Diverse" interview panels: This goes hand-in-hand with my next point (assessing for ALL skills in the job description). The interview panels should be "diverse" and the panel in its entirety should be able to assess all the skills in the job description. Moreover, the interview panel should reflect the current reality of the organization in terms of diversity. If the organization is predominantly male-dominated, then so be it...that's what the panel should be. Giving a "false sense of diversity" by having the one female software engineer do ALL of the interviews is not the answer. It would reflect badly on the organization in the longer run.
• Assessing for ALL skills in the job description: This is an important one, especially for a "technical" position. Very often interviewers tend to focus on the first few skills in the job description which are the "technical" skills. For example, does the person know javascript right now. The interviewer forgets to assess the candidate for rest of the skills mentioned at the bottom of the list - which are generally around communication, adaptability to learn new skills, working with a team, and so on (maybe these skills are harder to assess...?).
• Objective evaluation of the skills: Every interviewer should be forced to evaluate the candidate "objectively" by giving a score for every skill they are assessing (score out of 10 for example). Every skill should be evaluated by at least 2 interviewers.
• Objective evaluation of multiple candidates: After multiple people have been interviewed for the position (preferably by the same interview panel) - the scores should be tallied and the candidate should be chosen based on the final score.

You may have noticed that I've put the term "diversity" in quotes throughout the article. That's because the definition of "diversity" differs from person to person. I believe that teams should be "diverse" to be successful - because they have access to multiple opinions, life experiences, and hence perspectives. This would mean thinking about "diversity" in more than one terms: gender (that's the one that comes to mind naturally in tech), age, ethnicity, race, cultures...and any other aspect that comes to mind.