preventDefault is what you're looking for. To just block the button from submitting
<Button onClick={this.onClickButton} ...
code
onClickButton (event) {
event.preventDefault();
}
If you have a form which you want to handle in a custom way you can capture a higher level event onSubmit which will also stop that button from submitting.
<form onSubmit={this.onSubmit}>
and above in code
onSubmit (event) {
event.preventDefault();
// custom form handling here
}