Validate at least one of two TextBoxes must have value in ASP.Net using Custom Validator

You will need to make use of Custom Validator in this case.

HTML

<div>
    <table cellpadding="2" cellspacing="2">
        <tr>
            <td>
                Phone Number
            </td>
            <td>
                <asp:TextBox ID="txtPhoneNumber" runat="server" />
            </td>
        </tr>
        <tr>
            <td>
                Cell Number
            </td>
            <td>
                <asp:TextBox ID="txtCellNumber" runat="server" />
            </td>
        </tr>
            <tr>
            <td colspan="2">
                <asp:CustomValidator ID="cvMobileOrPhoneValidation" runat="server" Display="Dynamic"
                    ForeColor="Red" ClientValidationFunction="MobileOrPhoneValidation" ErrorMessage="Please enter at least one contact number."></asp:CustomValidator>
            </td>
        </tr>
        <tr>
            <td>
            </td>
            <td>
                <asp:Button ID="btnSave" runat="server" Text="Save" />
            </td>
        </tr>
           
    </table>
</div>
<script type="text/javascript">
    function MobileOrPhoneValidation(sender, args) {
        args.IsValid = document.getElementById("<%=txtPhoneNumber.ClientID %>").value != ""
                        || document.getElementById("<%=txtCellNumber.ClientID %>").value != "";
    }
</script>

Screenshot